"By a certain time" indicates that the action will have been COMPLETED by then. So the correction version is, "I have to be in bed by 10." "I have to go to bed before 10" is correct.

They are very similar and both correct. Basically have the same meaning. If you were going to meet with someone you wouldn't say I'll be there before 10 you would say I'll be there by or at 10.

Thank you, Heather!!

They mean the same thing. I think it is more a regional preference - in some regions 'before' would be more commonly used and in other regions 'by' but no matter what you use you would be understood.