Wireless charging Apple 13, is it compatible? Does it need to be set up?

Yes (MagSafe).

No. Just connect to the back of the phone.

How to use your MagSafe Charger with iPhone 14, iPhone 13, and iPhone 12 models - Apple Support

You also don't need to spend the money on an Apple charger if you don't want to. Any Qi-compatible wireless charger should work. I get them for about $20 on Amazon. With them, you plug them in, and then put the phone on the charging pad.