Can I restart my phone back to original date it was changed from old phone?

You can erase all of the data on the iPhone 15, so the phone will look just like it did when it was brand new out of the box.

Settings > General > Reset > Erase All Content and Settings.

But.....if you want to then transfer the data on the iPhone 13 to the iPhone 15 again, you will need to have the iPhone 13 or a recent backup of the iPhone 13.

No.

What you can do is : Go to Settings > General > Reset, then tap Erase All Content and Settings. Enter your passcode or Apple ID password. Wait for all content to be safely removed from your device.

How to erase all content and settings - Apple Support (IN)