a, c, d and e are fine.
I think sentence b sounds strange. I think this is because you have used the past perfect tense but have not clearly described a *subsequent* action in the way that you have done in sentence c. Instead, in sentence b, you have provided a statement about what time you went to bed - your sentence has not clearly located one thing after the other (even though this is obviously what you mean).
Sentence c is definitely correct. But sentence b should, I think, be re-phrased so as to use the simple past tense:
"There was a live ball game on TV last night, I watched it and did not go to bed until 3 AM.
By the way, just so that you know:
"Ball game," is only really used like this in American English. In the language of the UK and the Commonwealth we would usually specify the type of sport that you were watching.. For example "There was a football match," or "There was a cricket match..."