After/while running tests I make notes which I want to see in the Test Suite. Is it possible to add these as a column? It isn't visible as a column option. Now, I have to view results of every Test Case to see the notes...
Adding new column for Test suite depends on version of TFS that you're using. In TFS 2013 Test Suite is a work item like any other, but apparently there's no easy way to get additional information. Comment field (it's 'Description' in TFS, but it looks the same to me) can be accessed via pressing Ctrl+G ("Go to work item" window will appear) and fill in "Work item ID" field with Test Suite Id which can be obtained in the Plan or Test section after clicking on suite in the suites tree:
Note: AFAIK it's the resolution that doesn't work on TFS 2012 and earlier versions.