Is the apple watch compatible with Sky Mobile as they piggy back on the O2 Network

The Cellular + GPS Apple Watch shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:

https://www.apple.com/watch/cellular

Sky is not listed. NVMO need to have a come to an agreement with the underlying carrier and with Apple before they can support the Apple Watch. The above list of carriers are the ones that support the Apple Watch.

The GPS only Apple Watch can do Everything the Cellular model can do AS LONG AS your iPhone is nearby, where nearby is generally somewhere in the same moderately sized home. The Cellular model allows you to leave your iPhone at home while you go for a walk, run, bike ride.

No,Sky just leases O2'S equipment and are a separate company from O2.