Warranty

While the plan can be transferred to a new owner as the link javaliga proved, it cannot be transferred from one watch to another watch. If you own an Apple Watch, which is currently covered by a valid AppleCare+ plan, and you are buying a new watch, you cancel the plan on the current watch. If you are paying monthly, you won't be charged for the next month after you cancel it. If you paid for the plan in full upfront, you use this link and ask AppleCare+ Plan administration for a refund of the unused portion of the plan on the watch.

You then buy a new plan for the new watch.

See this --> Cancel or change the payment method for your AppleCare plan - Apple Support

Yes, you might be able to. See:

Transfer your AppleCare plan - Apple Support

Yes indeed!

Shows how a simple question can be interpreted in so many different ways.