I am looking to get a definite answer to title question.

Is there a set of rules that translates any program into a configuration of finite pieces on an infinite board, such that if black and white plays only legal moves, the game ends in finite time iff the program halts?

The rules are the same as ordinary chess minus the 50 move rule, exchanges and castling.

And what is the minimum number of different types of pieces (ie the simplest game) that is needed for a chess-like game to be turing-complete? (Each type of piece having a set of allowed moves that is invariant under translations)