Apple Care for Apple watch

Yes. See the following from AppleCare Products - Watch - Apple

How to buy

1. Purchase AppleCare+ with your new Apple Watch.
2. Or buy it within 60 days of your Apple Watch purchase:

• • Online (requires you to verify your serial number and run a remote diagnostic)
  • At an Apple Store (inspection of Apple Watch and proof of purchase are required)
  • By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

Almost certainly.

Buy an AppleCare plan [was: Can I buy an AppleCare plan for my device?] Click here --> https://support.apple.com/HT202702

Applecare+ for Watch

https://www.apple.com/support/products/watch/

You can also purchase AppleCare + at Best Buy.