What should I do to save information from a phone that might break?

You can plug your phone into your computer. You can there copy and save all your photos. For your contacts, you would go into your phone and you would click export contacts. It would create a folder. So when you plug into your phone, you'd be able to transfer all your contacts as well.

If you want a new shell and new motherboard, it would be $250 since you have a brand new phone.

Yes, you'd plug your phone into a computer, yes.