1. I don't know, never tried this. I do know iCloud backups still work, because I've used them after wiping my phone. But I think you must plug the new phone into your computer and set it up as a managed device before you load the backup, or else parts of the profile might not take.

2. No, it's not. I traded in my old macbook pro for a mac mini back in May. I was able to use Apple Configurator on the new mac mini to change the profile on my phone. There is one caveat though -- the phone is still technically supervised by the old mac, so you have to confirm the profile by going into the phone's settings. Using the original, you just have to plug the phone in and unlock it.