Hi H,
I'm not sure about this. Should be o.k. if you have good quality rim tapes, which I believe you have. The area of the rim tape which does not cover the spoke holes is greater than the area over the spoke holes, thus there is more pressure holding the tape against the rim than there is pressure stretching the tape into the holes. I'd say if in doubt, throw the old tape out and fit a new one.
There's probably a greater danger of a tyre blowout if the bike is left standing in the hot sun on a day of say, 35 - 40 degrees Celsius. Depends on age and condition of the tyre, too. When the bike is moving, airflow around the tyre is enough to prevent excess heat build-up.
For long-term storage, yes, I'd drop the pressure down from 120 psi.
Hmmm, just reading that first paragraph again reminds me of Pythagoras and his right-angled triangle: The square on the hippopotamus hide is equal to the sum of the squares on the other two hides.

Forgive me, I digress. It's been a hard week.
By the way, how are your new wheels?
Cheers. Will.