How can I link to query file that opens in SQL Server Management Studio showing database login window?
SSMS will not prompt for a login if you are already connected to an instance (e.g. Object Explorer), this is by design. If you want to change connections simply right-click in the query window and go to change connection.

Your request to include the username and password in the file somewhere is bad security. Especially if this particular account has elevated privileges to the environment.

If you are looking to automate the process, allow minimal involvement, allow anyone to execute the queries, and run them against any number of servers then I would suggest building the queries in PowerShell. A simple function that accepts say a server name and the script file can be written around using Invoke-Sqlcmd or .NET code if you are so inclined. Or write a function for each query and then just have them pass in the server name.


  somebody with very little knowledge


This is dictated by your documentation of your process. If your process is written to a 3rd grade level then any adult is assumed to be able to perform that process strictly by following your documentation.