Fix problems in ITUNES please - APPLE USERS?

I'm having an iphone 4s and i want to transfer movies from my computer to iphone

when i click on sync on itunes it shows me to remove and sync and it shows it will delete all my data (if i click remove and sync will it delete all my contacts, installed apps, images, songs, videos)

i have authorized three computers with my iphone

the problem is in first computer i can add movies and songs but apps are not copied

and in other two computers i can install and copy apps but unable to transfer videos and songs

Apple allows authorization only with one PC. I think that if you try to sync with other PC it will delete all media data, but not apps. Contacts, images will stay. And it sounds weird that you can't transfer movies and songs from one particular iTunes library. Why is that?
Keep all your stuff in one place or I think it is possible to back up the stuff on iPhone, just in case.