Philosophical questions in the modern world?

Plenty.

Is abortion, euthanasia, just war, eating meat, gay marriage etc. immoral?

what is morality for that matter?

If one is to create an instant transport machine, would it be the same person beamed to the other side?

what is consciousness?

what is required for free will?

what is democracy? equality?

Is induction based purely on habit?

this list will never stop..