Brute force alone is not very good for chess: you need some means of evaluating a position to prune your tree, otherwise you will not be able to plan very far ahead at all. The evaluation function is in large part what makes one chess engine better or worse than another, and nowadays that includes some neural nets for the top engines (stockfish, which is still the best AFAIK, uses a relatively small net and still evaluates some 100s of millions of positions, while Alphazero has a relatively larger net and evaluates about a thousand or so positions, and is also far better than any humans)
Brute force is good enough, at any given moment the # of possible moves is finite. The limiting factor is how much hardware you have and how quick you need the next move.
Sure, but unless you wanna wait a few thousand years on a pretty large cluster you're not going to get a chess engine that's gonna beat the best humans. The number of moves is finite but very, very large.
