For your first question, if you write "I will do this to 11:00" it doesn't make sense because it sounds like you will do something physical (hit it, cook it, shower it, or any other physical thing) to the time "11:00". That is impossible to do and that is why it doesn't make sense. "By" in this sentence is saying that you will do something before or at 11:00, which makes total sense. As for your 2nd question, your sentence should read: "Could I use TO instead of BY in the sentence below?" :)

"I'll do this by 11" means that you will finish something at 11 or before 11 the proposition By is mainly used to refer to a deadline, So its used to indicate time. You can't use To because to is used to indicate place or person. Example: I have to submit my assignment by 11. I have to sumbit my assignmet to my professor.