We need to allow users to check-out check-in files in Windows Explorer.
Is it mandatory to install Visual Studio in order to use Team Explorer or TFS Power Tools?
What kind of licenses will be needed?
You can install Team Explorer which is free (but still uses the VS shell), this doesn't require any kind of Visual Studio license: https://blogs.msdn.microsoft.com/devops/2017/04/05/reintroducing-the-team-explorer-standalone-installer/
Then you can install the TFS Power Tools to get the Windows Explorer extension which allows you to do basic source control operations in Windows Explorer.
Note: If you are connecting to an on-premise TFS you still need to purchase TFS CAL's. If you are using Azure DevOps (formerly Visual Studio Online) you get 5 users for free.