How often should I check rear derailleur adjustments? If I remove the (rattling)plastic disc  - 


How often should I check the limit screws on rear derailleur? 
If the shifter cable tension is less than optimal, would this be a possible cause to drive the chain in between the spokes and the rear cog-set?
Excluding the case of debris getting stuck in drive-train; are there any other adjustments besides above two and true-ness of rear wheel that may cause the problem of getting chain between cogs and spokes?


Derailleur in question is a Shimano Deore.

Update: Details- For mileage, I commute about 110 miles/week.
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)