Changing sim from iPhone 5c to Sony?

There's a bit of a problem. The iPhone 5c uses a Nano SIM card, which is smaller than the Micro SIM that the Xperia uses. You can buy a SIM adapter, but this is risky as if something goes wrong, it can tear the contacts on the phone, rendering it unable to accept a SIM, or to play it safe, you can get a replacement SIM from your carrier.

As for your pictures and other things, did you make a backup? If you didn't and the 5c no longer works at all, you can't do anything about it. You can't really transfer your messages as they're stored on the phone, pictures as well. Most phones let you store your contacts on the SIM card, but I think that you have to specifically choose this option.
So, if you don't have a backup of any kind, you're not going to be able to get any of your old info on the new phone. Sorry. Hopefully you understand now how important it is to make frequent backups.