When local bands play songs made famous by recognizeable artists, does that violate copyrights on the lyrics, music or the recording artist's performance and recording?
If so, why does it appear to go without consequences? Is it just too small, or do the artists (and everybody else involved with the originals) just accept it because it might help promote the songs?
Would these copyrights likely be enforced if another well-known artist recorded a recently popular song and started making some real money with it?
This part of copyright law is called "performance rights." In sum, it is copyright infringement to publicly perform another person's song. The wikipedia article has a good explanation.
It isn't practical to enforce this for performances in small venues, but as the performance is larger and/or more widely well you known, you should expect to get a nastygram from a copyright lawyer if you haven't received permission in advance.
Yes and no. It's a grey area without a lot of case law. A cover band that earns it's money solely based on another artist is still grey because they can be considered a parody act, but they won't always be.
There is common licensing available to venues and artists that cover a wide variety of music and it's pretty inexpensive. But even if you do have that licensing in place, not all artists will be covered, nor all songs from all artists.
I would be concerned if any of the following were taking place:
1) The band or the venue's revenue was centered around cover work.
2) The revenue is significant.
3) The audience is significant.
4) Media coverage is present.
5) Advertising is present that specifically mentions work or artists to be covered.