Can you take online college courses without a high school diploma or GED?

Yes, if you are looking forward to be in teaching profession and you have completed your +2 successfully, you may opt for teacher training courses. I would recommend you to visit Asian College of Teachers for the same.
Yes, you can. As long as you are over 18 you should be able to take classes. Realize, at some point they may tell you to go further you need a GED. Get a GED and once that is done move towards a college degree.
Yes, I know the community college system allows high school students and people without GED to take classes.