In Conway's Game of Life, would a cell be considered a deterministic finite automata? Is there a language for the automata, and would it be a regular language?
In probabilistic cellular automata, are the cells considered nondeterministic finite automata, Is there a language associated with this as well, and is it too considered a regular language?
Too long for a comment.
If you wish to express a single cell to be expressed as finite automaton (and provide the connection between them in some other way), then with some particular choice of input it is possible to encode as a regular language. For example, each step the automaton could be feed 8 symbols $0$ or $1$ that represent the state of its neighbors (and knowing if it had accepted or no the previous turn, it could accept or not at current step).
On the other hand, if it were to work "by itself", then no, Conway's Game of Life is Turing-complete, and as such impossible to express as a finite state automaton. The space for Conway's Game is infinite, so it still might be possible to express it with some infinite state automaton, whatever that is.
I hope this helps $\ddot\smile$