How often should I check rear derailleur adjustments?
It's really up to you how often to check your adjustments, but I'd say it's not an "every ride" kind of check, unless you're giving your drivetrain a workout! If there's any damage to the derailleur, hanger, or rear wheel, you may want to start there as well. 

To specifically address your questions:


You should check your limits any time you have a drivetrain issue. That could be poor shifting, dropped chain, or inability to shift.
Shifter cable tension should only affect how easily/quickly the derailleur moves. However, there could be a case where too much tension could cause the derailleur to move through the last shift enough to stress past the limit screw, but I think this is unlikely.
The rear wheel could be out of dish (centered from side-to-side) which might have moved the cassette further in. Readjusting the limit screws should take care of that, but you might still have shifting issues. (I had the same problem this spring)