They don't mean the same.
"你去干嘛?" means "What are you going to do?" or maybe "Why are you going?" depending on the context.
"你去吗?" means "Are you going?"
A: 我出去一会 = I'm leaving for a while. B: 你去干嘛? = What are you going to do?
A: 我去开会了 = I'm going to attend the meeting. B: 这会是给经理开的, 你去干嘛? = The ...
'要' in '不要' cannot be removed, because '不要' is a compound word that mean 'don't'(auxiliary verb) which is different from '不' (adv: not)
不要说话/ 别说话 = Don't talk (demand)
不说话 = 'not speak'
看电影的时候请(不要)说话 - Please (don't) talk when watching movies (O)
看电影的时候请(别)说话 - Please (don't) talk when watching movies (O)
看电影的时候请(不)说话 - Please (not) talk when watching ...