It appears one would go to idle thrust at touchdown (mains),
Well, usually at some height above touchdown, like 30 feet or so...
and following nose-wheel touchdown (I'm assuming a squat switch)
Actually it varies, on the 733 it is at the earlier of 10 feet on either radalt, or air/ground logic (i.e. squat switch) activation, and the thrust levers at idle (the reverse levers won't rise unless the thrust levers are at idle.
the levers are pulled up and back to activate thrust reversers with the engines at idle.
Yep.
Is it common to spool the engines back up while in reverse thrust
This depends on company procedures. Using reverse thrust puts a little stress on various aeroplane bits, so some companies ask for idle reverse, unless the situation demands othersie (like a wet runway). An interlock will hold the piggyback levers at the first detent until the reversers are at least 60% deployed, after tat you can pull the levers back to increase reverse thrust. The amount of reverse thrust permitted to you varies with the aircraft and engine combination.