As for the first question, you can do homework wherever you feel both comfortable and productive. I usually do my homework at my dining room table or sometimes I do it laying on the couch. But there are other times when I know I really need to focus, and on those days I go to the library. My point is, you should do homework where you are comfortable but also avoid distractions. If you know that when you’re at your desk it’s time to do homework, then that’s a great place to work.
To your second question, I think that strictly academically speaking, it’s okay to take classes online in subjects you are strong in. I’m currently taking my math class online. That said, I do have a couple reservations; first, with your tendency for procrastination it may not be the right decision to take a class online. Taking a class online requires a lot of motivation and discipline because you usually go at your own pace. You don’t have a teacher on your back about late work or other students to answer to when you don’t pull your weight on a project (not saying you do either of these things, just that they are ways people are held accountable in normal classes). I’d try to work on the procrastination tendency before taking a class online. My second question would be why do you want to take classes online? I think it is generally better to take a class at school if you have a reasonably decent teacher because it’s easier to get help, easier to be focused in class, and you can do different types of learning (like activities).
My 2 cents…