I always root stuff right after i get them (Note 2/3/4,Shield TV,S7) not had a problem yet.
I also buy phones outright and not through contract if that makes any difference.
No you can install twrp with orginial firmware, Follow the XDA TWRP post and it explains it pretty well.
Ah I remember now. I ended up using cf auto root because no matter what I did, during the flash I couldn't boot to recovery before booting up.