I'm positive I've never seen anything like it in Max. No checkers, backgammon or Monopoly either. I guess Max wouldn't be my first choice when building these, as there's lots of rules and a complicated GUI. 'Everything' can be done in Max though.
To help you on your way, here's the movement of a knight. I'm sure you can improve on it!
Nope, but you can talk to most modern chess engines via a terminal interface (UCI and WinBoard are the two most popular protocols). You can certainly rig something up with the 'shell' object to do this, or there might be some other ways to handle it.
If you need a good, free, MacOS UCI engine, look up "Glaurung Chess" in Google. On Windows, there are lots of options.