In this sense, OUP's '5 big questions' are philosophical for native speakers of English but not necessarily so for others.
Do we have free will?
Panini says 'svathanthrah karta'- the agent is always free. Thus for Indic origin people like me this is not a philosophical question. Rather it is a meta-metaphor. It is 'common knowledge' that Speech is necessarily configured such that will is free and imputed to any subject of a verb. Thus 'Free will' is merely a tautology with a certain allusive & expressive force. That expressive force makes it a metaphor for something else- viz. feelings of frustration amounting to ontological dysphoria. A meta-metaphor can be created by taking this feeling of ontological dysphoria as something fundamental and constitutive rather than reactive and contingent. The result is that a mood replaces the mind that felt it. Thus the question 'do we have free will' translates as- 'is the mood which has displaced the mind that produced it a Panninian agent? Do moods do things independent of minds?'
For even quite crap Hindus like me, the answer is 'D'uh!'
From childhood we think of the entire Mahabharata as having to do with 'manyu'- a mood of dark anger. We can say of each character 'not he did this, but his dark anger did so causing his antagonist's dark anger to do something else.' All events can then be seen as the unfolding of a univocal dark anger which usurps the minds of all agents till, in the 'night slaughter' of the Sauptika (sleeping) Parva, manyu is embodied as Kali. The resulting epic tableau is compelling as literature. Artistically, it could not be otherwise.
However, it is purely meta-metaphorical. It has no connection with reality. It is 'Maya'- wholly irreal- and not philosophical at all but psychological and literary. Why? Because now there is only one 'correct' answer- viz. uproot the tree of dark anger, even though the first step to doing so is cutting down the hymn leaved banyan whose roots are in heaven and branches here down below.
Both the epic poet depicting a great battle and the 'Lord of Yoga', or preceptor, who is seeking to dispel 'vishada' (abulia or akrasia) are constrained in advance. Thus any answer they give can't be 'philosophical'. It can be that of a free agent- but not a wholly self-regarding one. After all, an agent may freely choose not to be a principal but to discharge a duty of a delegated kind. That is the choice both Krishna Dwaipayana, the author, and Krishna Devakiputra, the Lord of Yoga, are constrained to make in the Divine Song though both suffer for it.
This, of course, is the secret of the universal appeal of the Bhagvad Gita as well as the larger work it is contained within. But it is 'itihaas' not 'upanishad'- a constrained path, not a lifting of horizons. Thus, I see the Mahabharata as a 'normal form' game-theoretic gedanken- something economic, not philosophical. In other words, 'robustness' (which must be the same thing as Muth rational 'naturality' or non-arbitrariness) though based on uncorrelated asymmetries is ergodic because of rational 'antidosis'- i.e. mutually beneficial, or otherwise equitable, exchange.
By contrast- to, not the Curry, but Cockney part of me- the question of free will is perfectly philosophical. Why? There is here a symmetric 'meta-game' because the first order game has multiple competing extensive forms at least some of which are equally 'good' or compelling in the same manner.
Free will, in English, is not a tautology at all because there is no Paninian moment in Western philology. It is not the case that 'common knowledge' re. linguistic convention has given the 'free will' language game a particular normal form.
When looking at old Western ideas of metempsychosis- tuirgen, treading the weird etc- the affective aspect has both a positive thaumaturgic valency- the 'trickster' Druid who has fantastic adventures and gains mastery over the elements- as well as a tragic valency associated with the too mighty warrior whose battle rage has destroyed his own world. Thus 'free will' is not so much about a mood as it is about the facts of the case. Thus there is no 'normal form' of the underlying game- it can only be 'extensive' and feature uncertainty, non-commutativity, asymmetry etc.
Thus in material terms, for the West 'free will' is a philosophical and chrematistical question. For India, it is a psychological and economic one. This does mean that, for Hinduism, Freedom is an ever Orient horizon. The bitter lees that, for Matthew Arnold & Andrei Weil, the Gita revealed to lie at the bottom of Freedom's draught (Yatha-ichasi-tatha-kuru 'Do as you please') can never become the whole of the Law even for this worthless ersatz Cockney cunt wot lives down the road from where Yeats stood vigil against, the Beast, Aleister Crowley. Which reminds me, coz of COVID, its been ages since I had a slap up British Breakfast at 36 Blythe Road. The yolk of a fried egg is all the Golden Dawn I need- provided there's buttered toast and plenty of sweet tea. On the other hand, my Doctor might not agree.
Can we know anything at all?
This is a univocal philosophical question for India and the West- indeed, Pyrrho is supposed to have accompanied Alexander to India and thus a common Jain provenance is plausible.
Simply put- any argument used to show that we can know at least one thing can be recast to defeat itself. How? Well, if we truly know one thing then we know how it is connected to everything else because knowledge connotes something stable and holistic not partial or in flux.
The problem here is that to know one thing entails knowing everything else unless we live in an occassionalist universe or one not composed of dynamically interconnected reals.
Suppose we say- 'but the thing is only connected to me- I know it and that's the end of the matter.' then, the rejoinder is- 'if you truly know it and it is connected to you, then you must know everything about yourself- including everything regarding your reaction to what I am about to do to you. But in that case you can either read my mind or know everything relevant about me in which case you must also know about how I am related to everything else. Thus if you truly know one thing connected to you then you must also know everything about everything!'
You may reply 'I know one thing- and the thing I know about it is that it has no knowledge content.'
This does seem to open the door to a shite sort of 'metaphysics' of an obviously bogus kind but not really because this knock-down argument can itself be knocked down because it presupposes that the you know one other thing which has non zero knowledge content- viz. that you can discriminate nothing from something.
More generally, to defeat any argument, it must be the case that at least one thing is known. But this is itself a self-defeating argument otherwise everything would be known.
At this point, I should make a caveat. We could have a 'common knowledge' based language game, or protocol bound system of defeasible reasoning such that the point raised in the last paragraph would lose salience. However, for this 'common knowledge game' or system of 'artificial reason' to amount to 'justified true belief' would require a proof regarding the Continuum Hypothesis. Interestingly, it doesn't matter if the proof confirms or rejects C.H. All that matters is that it be apodictic. Why? If there is justifiable 'common knowledge' then there must be a certain sort of metric involving cardinalities we currently 'know' nothing about. Once there is a metric then there is an algorithmic adjudicative 'buck stopping mechanism' for which no proposition is essentially self defeating because it can always be repaired.
In practice, any discipline which has an associated 'open question' in mathematics is subject to an epistemological problem related to this question. Why? Because, any empirical determination of a model's validity involves a non-commutative operator such that either entanglement or path dependency arises. In other words, verification imposes a cost on the theory. Generality has to be traded off against significance.
However, once an open problem in maths is solved- for example if we had a proof for P not equal to NP- then there is a 'buck stopping' mechanism for every discipline with relation to the epistemological problem associated with that previously open question. Thus it ceases to be philosophical and becomes technical or one for which there is an overlapping consensus.
Philosophy's 'distinctions without a difference'- in Collingwood's terms- are extinguished when a discipline finds a difference which corresponds to that distinction. A good example is Kantian 'incongruent counterparts' and the manner in which the Wu experiment changed that debate into something purely in the realm of Physics or, at worst, its associated Phenomenology which waits upon technical developments but is not itself Philosophical.
I have said 'can we know anything at all' is philosophical for Greeks and Indians or any culture which associates knowledge with seeing since our eyes can deceive us. For the Chinese however it was the heart, not the eye, which seeks and confirms knowledge. There is still a question here but is substantive and fecund, not sterile or merely philosophical.
Who am “I”?
Philosophically speaking, this question is the dual of 'why is there something rather than nothing?' Any answer one gives could equally easily have the opposite valency. Thus to say 'au fond, I am a machine' is to have provided the argument for 'au fond, I am a God'. Indeed, so to speak, the Higgs field of this discourse, by which arguments gain weight, has zero as a saddle point- thus it is vanishingly unlikely that it will contain nothing rather than something.
Nothing we can know or not know. It is 'Aviveka' for beyond the scope of 'Viveka'. However, in English, death could have a gnostic component. Indeed, since corpses are buried, not cremated, they might pop back up for a chat which is cozy enough till you realize the dude has fangs. Fuck me! It's a vampire!
A shit-show of a 'samskar' unless this planet knows it has to compete with other jurisdictions on a Galactic scale. Indeed, as Laffer pointed out, the knowledge that potential competition exists in the configuration space is enough for this outcome- provided gaining a rent didn't so irrevocably rot your brain. In other words, competition is something we have to actively promote. It is a different matter that coordination games will yield 'convergence'- but that is 'spontaneous order' not some conspiratorial, monopolistic, cabal at work. Anyway, Order is not Justice. It is merely a poset which has no 'natural' Spilrajn extension- till, perhaps, the End of Time.
For now, and forever, Justice, like Organised Religion, is a Service Industry which, if it has a captive market, goes in for discriminatory market segmentation- i.e. a fucking horrible caste system- so as to extract more and more rent till the country is conquered or otherwise rendered abject. Thus Religion, to survive, must itself hold as its highest good, release from its own bondage. As Vivekandanda said, it is good to live within the confines of a Religion. It is bad, from that Religion's point of view, for you to die in that, or any other, bondage.
It is a good thing that competing protocol bound juristic systems have arbitrary shibboleths and Kafkaesque principles of 'artificial reason'. The fact is, where there is an uncertain and shifting fitness landscape, there is no knowable 'naturality' available for Category theory. Thus, if we have to have a bunch of useless pedants gassing on about Ideas of Justice, then they may as well be Bengalis coz us Hindus both take pride in their putting one over on Whitey, as well as heartily loathing them for the manner in which they shit on our common Religion when, given their gifts, they could so easily do the opposite.