Wow. Where should I start.
The App store is free to register, it's up to you if you want to pay for the paid apps or you could just download the free ones.
To sync songs/backup, yes you need iTunes.
Jailbreaking is just a term letting you free up the limitations on your iPhone.
Honestly, do a search for any other questions, they should be all answered in this thread:
http://www.revscene.net/forums/iphon...e-t534336.html