How do I use Skype for Xbox Series X|S or Xbox One?

No, an Xbox Live Gold subscription is not required to use Skype for Xbox. However, you will need a Skype account. If you have a Skype account, you can sign into your Xbox using the Microsoft account associated with that account. If you don't have one, you can sign into your Xbox with the Microsoft account that you use for Xbox Live, and we'll create a Skype account for you.

Skype works with the quiet settings on Xbox, so you can control when friends and family can contact you on Skype. You can also choose to have a Skype call running in the background while you play games or use apps, and your video calls will automatically come in as audio only calls so you won’t be interrupted.

No. Snap mode isn’t supported with Skype for Xbox.

Select the menu  button. Select your avatar, and select Sign Out. When you launch Skype the next time, you'll be signed in again automatically.