1
I have to send my application until Friday.
I have to send my application by Friday.
Use by for a deadline: the application must arrive on Friday or earlier. Use until when an action continues up to a particular time: ‘The office is open until Friday.’
2
I will stay at the library until it will close.
I will stay at the library until it closes.
After until, use the present simple to talk about the future, not will: ‘I will stay at the library until it closes.’ See our lesson on future time clauses.