Assistance needed with formulas dealing with Dates & Categories

Attached is a small section of a excel spreadsheet data base that I can not seem to get the formulas to work at all or not provide the correct answers and I've tried everything I can think of
and that I've used elsewhere before all just didn't work.

There is a text box box on the sheet that explains what I'm trying to accomplish but I'm at a dead end till the issues can be resolved.