#251
Solving chess = proving that black has at least 1 move that draws against every sensible white move.
No it isn't. Solving chess is, among other things, determining if that is the case.
#254
A position with castling rights is different from a position without castling rights. A position with possible en passant is different from a position with en passant possibility. It is counted differently as such in the 3.8125 legal chess positions. See also
https://en.wikipedia.org/wiki/Forsyth%E2%80%93Edwards_Notation
One assumes you meant to say 3.8521*10^37 or 3.8521*10^39 depending on whether you intend to solve it under basic or competition rules (on which point you seem to be ambivalent). But you really need to stop referring to those figures as representing legal positions. We've already established they don't.
The best estimate for legal positions would be a little under 10⁴⁶ under basic rules or a little under 10⁴⁸ if the 50 move rule is added to the basic rules. (Over a quarter of an American trillion times larger in either case.)
#266
No, not at all.
There are 2 different things: 1) assessing the feasibility of solving chess and 2) solving chess itself.
1) To assess the feasibility we must estimate the number of legal, sensible, and relevant positions so as to estimate the resouces required i.e. CPU time on cloud engines. So the estimate should exclude illegal positions, non sensible positions like random samples from the Tromp count, and non relevant positions which are legal and sensible, but which will become unreachable in the course of the calculation, e.g. all positions with a white pawn on e2 after 1 e4.
2) To actually solve chess the cloud engines calculate from a humanly prepared 26-men tabya e.g. C67 towards the 7-men table base.