The rule you need for questions is:
If there's an auxiliary verb put it in front of the subject to make the question. If there's no auxiliary, put DO in front of the subject to make the question. Don't use DO if there's another auxiliary.
does staring at this will hurt my eyes?
does teaching will make me more patient?
The subjects in your sentences are staring and teaching. The auxiliary you should have is will (if there's another auxiliary, we never need DO!). To make the question we move the auxiliary in front of the subject like this:
- Will staring at this hurt my eyes?
- Will teaching make me more patient?
[There are some special questions called subject questions, which are different. You don't need to worry about those - because students almost never make mistakes with subject questions!]
Hope this helps!