Learn English – Do I need to use “guess” or “try to guess” when I want someone to try to anwer the question

Here are some empirical results.

Corpus Of Contemporary American English:

• WITHIN THIS WEEK: 2 hits
• BY THE END OF THIS WEEK: 58 hits

BYU-BNC: British National Corpus:

• WITHIN THIS WEEK: 0 hits
• BY THE END OF THIS WEEK: 7 hits

We can conclude from that that "by the end of the week" is much more common in both American and British English, and thus it is also probably much more natural.

In U.S. English, the simplest way would be to ask

What time does she get off work?

A shade more formal would be

What time does she usually leave work?

or

What time does she usually leave for the day?

In the latter, the work context would be understood. Don't use it if there could be some confusion.

Here's one way to ask involving the word stay:

How late does she usually stay [at work]?

Be careful, though, because any of these might be construed by the listener as evidence that you may be nosy at least, and possibly a stalker. So unless you're checking up on this woman as a job applicant, the prudent course would be to ask her yourself.

addendum for OP

You asked where you should place the until in your constructions. Presumably you're wondering whether you should avoid putting it at the end of the sentence. The answer is: don't avoid that. While some pedants will wince at this, they really don't have a leg to stand on. See this accepted answer on ELU to the same question. (TL;DR: This is a rule made up hundreds of years ago by fussbudgets who determined, against all usage evidence to the contrary, that English should behave more like Latin.)

Therefore you should feel no qualms about asking

What time does she work till?

or

What time does she work until?

But since English is pretty flexible, you could also easily say

Until what time does she work?

But for my money, that sounds a little more formal, even stilted.

Note that till and until are pretty much interchangeable here. See this related discussion on till and until on ELU.