Two verbs in one question

Good day all…

How can I manage two verbs in one question ? like the followings :

Did you think that the professor does not know our names?

Why does the teacher stop the lessons when the student entered?

Why does the teacher stop the lesson and chased the cat in room?

Does he know you did not live there?

Why did she shout at him and closed the door ?

Is that true I changed only one verb tense, and the other one is like the origin in the sentence?
How can I manage the tenses?
Can i apply the auxiliary (do, does, did) to both of them ?
How can I know which (verb) to be changed not the other one?

thanks in advance

Did you think that the professor does not know our names? <-- this could be okay if the intention is to ask about what someone believed in the past about a situation in the present, but is unlikely. Usually it would be:
Did you think the professor didn’t know our names? (past)
Do you think the professor doesn’t know our names? (present)

Why does the teacher stop the lessons when the student entered? <-- This is only correct in a situation such as where someone is showing a video of a teacher stopping a lesson (not ‘lessons’) and asking someone else why the teacher stopped. Usually the sentence would be:
Why does the teacher stop the lesson when the student enters? (present)
Why did the teacher stop the lesson when the student entered? (past)

Why does the teacher stop the lesson and chased the cat in room? <-- This is incorrect at all times.
Why does the teacher stop the lesson and chase the cat around the room? (present) (Why does the teacher stop? Why does the teacher chase the cat?)
Why did the teacher stop the lesson and chase the cat around the room? (past) (Why did the teacher stop? Why did the teacher chase the cat?)

Does he know you did not live there? <-- This is okay. You are asking now about an event in the past.

Why did she shout at him and closed the door ? <-- This is incorrect at all times.
Why did she shout at him and close the door? (past) (Why did she shout at him? Why did she close the door?)
Why does she shout at him and close the door? (present). (Why does she shout at him? Why does she close the door?)

Mrs. Beeesneees

Thanks lot, and I am grateful

Now I think that is we have two subjects and two verbs we only change the tense of one verb. When i have two subjects and two verbs I must deal with each verb separately. Am I right?

These questions we have two subjects and two verbs.

Why does the teacher stop the lesson when the student enters?
Does he know you did not live there?
Do you think the professor doesn’t know our names?

But these are different:

Why does she shout at him and close the door?
Why did the teacher stop the lesson and chase the cat around the room?

Thanks in advance

That’s well observed.

Mrs. Beeesneees

Thanks a lot… I am really grateful…

Bless you

I have no further question