cosmonauticus,
1. No worries either way. Recording studios tend to leave their gear on 24/7 because cycling the power does tend to wear out electronic stuff more than leaving it on. On the other hand, a good power line spike in the middle of the night from a thunderstorm could cause it to let out the magic smoke and then you're in trouble too (once you let that smoke out, electronic devices tend to quit working

2. Well, if you're really paranoid about it, go get an adapter with a male 3.5mm plug at one end and a female of the same on the other. Then plug the headphones into it. That way you'll be wearing out the adapter instead of the headphone jack on the HDP.
No matter what though, the most important thing to remember to do is...
Have fun!

-Bob