Could people such as Einstein solve the unsolved mysteries of the world if they were still here?

I would like to think that the answer is yes. They should have gained some additional knowledge that would round out their original genius!!!

No.

No. Not unless they had a shift in ideology.
Einstein famously rejected quantum mechanics because “god does not roll dice”.
Newton likewise could not reliably predict the movement of planets long term due to perturbations of their motions by the gravitational pull of other planets, and he gave up by claiming that god literally kept the planets in their orbits.

I have no doubt that as scientific evidence challenged their beliefs that they would have revised their thinking and resolved some of the scientific issues challenging scientists today. In the process, they would also identify new conundrums in scientific understanding. The more that is known, the more one knows what they do not know.

I suppose so if he was upto date with some results and experiments as in the present.
Here is a link to some of those unknowns.
https://www.livescience.com/34052-unsolved-mysteries-physics.html

Someone will.

No. Remember that E=mc squared is a theory.

What if certain questions in physics are ultimately undeterminable? Would that necessarily be a bad thing?

No. There is always another question.

I don’t think it rolls down to a single person’s brain power. Also, Einstein and Newton were focused on different areas than P=NP. Galileo has his focus too.