Can I downgrade iOS on iPhone 13?

Apple does not support or provide a path to downgrade iOS. They are no longer signing anything below iOS 18.2. You certainly could not go back to iOS 15, which is what the iPhone 13 shipped with.

No. You can only install the highest iOS version currently supported by that device which is iOS 18.2 If you wanted, say, iOS 15, you would have to buy an older phone where that was the highest version it could run.