This is wrong. When you usually do something, then you have to add "Om" . Fx. Han synger sammen med dem om tirsdagen og torsdagen
That's exactly what I typed out. My Danish is still pretty bad, but this seemed most grammatically comfortable to me?
Why isn't it om tirsdagen og torsdagen? I thought that that is what you put for the habitual.
Why is it tirsdage and not tirsdag?
Because it is plural.
English sentence is incorrect. It should be "He sings with them on Tuesdays and Thursdays" or "He sings with them all (day) Tuesday and Thursday". Otherwise it does not make sense.
The English sentence is perfectly correct in my dialect of US English.