Good day!*
can I use the iTunes to sync video!,applications,etc to my iPhone after jailbreak and unlock
with redsn0w- ultrasn0w without worrying to get some error with it? can I purchase and
use app store or itunes store normally after jailbreak and unlock?
PLEASE GUIDE ME SOME ONE!?

with uber skillz

You could also get a phone that does all this stuff without having to jailbreak it. They often come cheaper and give you more control over what you do with your phone, too.

edit: and oh yeah, it's illegal to ask about jailbreaking your iphone here. In fact, it should be illegal to talk about iphones anywhere.