Loser chess has a benefit of sorts. There are many turns where moves are forced. So my question is, has it been solved? I'd say that the move tree is much smaller than chess. If not:
Professor Mark Watkins announced he had found the solution to Losing Chess in October 2016. Regardless of what Black plays, White can force a win beginning with 1. e3.
To the third question: yes, there are. I found one, at least. This page should interest you. It has some articles, proof trees and is updated regularly, it seems. The articles and files on the page also give some indication as to the first two questions, for example the number of nodes and size of the proof tree files.
It appears that game as a whole is not solved, but some of the more common variations are. There are also some endgame tablebases available.
Remember, as one comment stated - many moves in the game are not forced, thus vastly increasing the number of possibilities.
For question 3, just as GloriaVictis said, losing chess is almost solved. Only 1.e3 b6 is still being solved now. All others have already been proven to be a black loss. Based on how fast each response to 1.e3 (generally at most several months) is solved I believe we will see the solution of losing chess this year.
Also the solution is likely to be a white victory. For your first two questions they will be known after losing chess is actually solved.
P.S.: I'm following Prof. Watkins' research almost daily so when losing chess is finally solved I will post an answer here.
