How to connect an existing repository with bitbucket to a project in Visual Studio, and manage changes from the studio?

Answer 1, Authority 100%

Come in the repository on the Bitbachet, in the menu on the left click on the Clone, select HTTP and copy the link (similarly for Hithab / Hitlab / any other repository – need an HTTP link to the repository):

Then in Team Explorer choose the creation of a new repository:

In the Local Git Repositories section, select Clone, specify a link to the repository and where to clone: ​​

Ready.