If i restore my new iphone from backup, will it delete what i currently have on it?

I had an appointment at the genius counter at the apple store on sunday because the lock button on my phone was broken blah blah blah… Anyway, i had no idea that they would give me a brand new phone? I took some pictures and videos on the new phone that i'd like to keep though and if i restore the backup from my old phone from itunes, will it delete/replace these pictures?

You don't ever have to shut an iphone off. Just let it go dormant and if you want it silent, flip that corner switch and don't turn it off. It doesn't lose power when it goes dormant and I don't think I've had mine off in 2 years now.