Stalemate

Does anyone know how stalemate affects your ratings?

Same points as a draw, if you're the lower-rated player your rating goes up, the higher-rated player goes down.

Actual points depends on rating difference, there's a ready reckoner in Thread 80000.

Does anyone know at what point the game acknowledges a "stalement" due to repetitive movement, or extenuative chasing?

(i.e., Isn't there a rule like, "can't move back-&-forth between the same spaces more than 13 times" and/or "if chasing a king, and no checkmate after 55 moves, then stalemate.", etc.?)

Originally posted by Belltron
... a "stalement" due to repetitive movement ...

A "stalement" is never due to repetitive movements.

http://en.wikipedia.org/wiki/Stalemate

Originally posted by Belltron
Does anyone know at what point the game acknowledges a "stalement" due to repetitive movement, or extenuative chasing?

(i.e., Isn't there a rule like, "can't move back-&-forth between the same spaces more than 13 times" and/or "if chasing a king, and no checkmate after 55 moves, then stalemate.", etc.?)

You should review this section of the FAQ to better understand drawn game conditions. FAQ

Here is the wiki definition of stalemate: "Stalemate is a situation in chess where the player whose turn it is to move has no legal moves but is not in check. Stalemate ends the game, with the result a draw."

If a stalemate occurs, the software will recognize it and end the game.

If the conitions are met for a drawn game as defined in the FAQ section above, one of the players will have to claim a draw.

Also if either player offers a draw at any time, the other player may accept or decline the offer. There are no situation requirements needed to make a draw offer.

I hope this is of some help for you.