Can it also have another meaning like this - Suppose I am living (alone) by myself. In this situation can I say -
1. I cook by myself?
2. Or should I say - I do my own cooking.
3. Or, I cook for myself?
I think I can say 2 and 3. Would 1 be also OK?
I feel slightly differently than Gil.
1. Emphasizes that you have no one else in the kitchen with you.
2. The normal way to say you don't depend on anyone else for your meals.
3. Could be #2, or as Gil says, that you don't share with anyone else.
Let's say you have a friend over, and he's helping you get your dinner together by peeling vegetables. You can still say you do your own cooking (compared to eating out or having your mom bring you meals) if he helps you, but you cannot say that you cook by yourself if your friend is doing any of the work. And if he shares the meal you just prepared, #3 won't apply.