Close a work item via the commit message

Finally in 2019 they implemented this as a a light version of gitlab.

Using the keyword fix, fixes or fixed #ID will close the Workitem.

Detailed instructions: https://docs.microsoft.com/de-de/azure/devops/repos/git/resolution-mentions?view=azure-devops

No, there isn't any way to do this for now.

Similar question: TFS git commit change work item status

Feature request on VSTS User Voice: Update work items on commit for git