the hardest problem in chemistry is protein folding problem.
There is no real "hardest". It all depends on what you are good at and what you are not good at. There is no way to determine a hardest.
I am pretty sure you can make them as hard as you want - if you have a "hard" problem, you can always find one that is even harder. If this is true, then there is no such thing as a "hardest algebra problem".
Immortality.. I supose.
Proving the Riemann conjecture.
That's hard to say.
stating the problem and then designing the experiment.
Anyone can if they work hard at it.
Depends whats hard for you.
5 + x = 6