can I carry my AppleCare over to my new iPhone 14( 4months left on my iPhone 12 mini)

See instructions in Cancel or change the payment method for your AppleCare plan - Apple Support

and also see the following from AppleCare Products - iPhone - Apple

How to buy

1. Purchase either AppleCare+ product with your new iPhone.
2. Or buy it within 60 days of your iPhone purchase:

• • On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)
  • Online (requires you to verify your serial number and run a remote diagnostic)
  • At an Apple Store (inspection of iPhone and proof of purchase are required)
  • By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

No. You can cancel it and receive a prorated refund if you paid for it all upfront. Then start a new plan on your new iPhone