Hello, great stairway!
I have two instances of SQL server installed, 2008 R2 SP1 and an EXPRESS version I think installed with Visual Studio.
I am able to navigate to
SQLSERVER:\sql\localhost\SQLEXPRESS and even to
SQLSERVER:\sql\GARUDA\SQLEXPRESS (GARUDA is the computer name)
and see the databases as in your examples but have not been able to navigate to the other instance, or to even find what the instance name is, unless it's MSSQLSERVER (which it does not recognize)
I do not do anything with SQLEXPRESS, so can you tell me how to find the instance name and connect through PS?