It depends on where the movie is being shot, the budget level, and whether or not the production company has a contract with SAG (Screen Actors Guild). SAG has different rules for L.A. and NYC than say Chicago or Philly.
There are people here in L.A. who actually make a living as an extra, especially if they become a regular background on a TV show. For instance, on "Star Trek: Deep Space Nine", many of the background patrons of Quark's bar were the same people for the entire run of the series. The character of Morn was the same guy in a full suit and mask for the seven years the show ran. I don't think he had any lines because then he wouldn't have been an extra anymore and would have been paid more money.
If the production isn't a SAG signatory, then they can pay anything or nothing but meals.
editted to actually answer the questions asked:
Extras do not get residuals.
As stated above, you can get away with just feeding the extras, so it can be pretty cheap.
Don't know about "extras" for the stage. That would fall under Actors Equity, the union for stage actors. But I'm sure there is a minimum for even the guy playing the butler on Broadway.
Here's a web page that gives good info
About Extras