They are all correct or valid. The difference in meaning, if any, is very subtle indeed.
To me, the dancing, cooking and singing cases -- if they were all in the past tense (and I realize they are not, but bear with me) -- are suggestive of a shorter period of time, as if I did not witness the entire event. The dance, cook and sing cases -- again, if they were all in the past -- are suggestive of a longer period of time, as if I witnessed most of the event.
If they are in the present or future tenses ("I am..." or "I will..."), then the dance, cook and sing cases just sound better to me.