1: 5子棋 on a 15x15 board has been solved, by AI guy in case you care, and proved that black (first to move) win in a perfect game, JFF is too stupid to know it, and to learn.
2. The fact is most of the problem is "not" NP or #P. There are more problems in a bigger harder problems. As a matter of fact, there are more unsolvable problems than solvable problems, way more. Unsolvable problem is uncountable.

as for 3 and 4, these are not scientific questions, and they are too vague to be comment on.