Are H1B/F1 peeps allowed to do overtime?

As far as I know, F1 OPT allows as long as DSO is convinced that you are working to augment things learned at school

Most intern programs don’t want interns working overtime and explicitly tell them not to.

U can’t work over time

Yes. But your manager may not approve overtime.

You can work as many hours as you can but you will be only paid for the limited number of hours as per visa status.

I believe you can get overtime, as long as manger approves it. ( I'm not sure though)

You're an intern.. have some fun

You shouldn't get into the habbit of working overtime, and managers receiving interns are told to ask questions if someone is working too many hours. There will be plenty of companies happy to burn you out after you graduate