Omission of the relative pronoun

I would like to ask if omission of the pronoun in the relative clause in this case is correct,or it must be pronoun he included.
My dad got a new job,and was obliged to change the place of living.
I also would like to know some books in which I can find information on this topic.
Thank you

Tu nie ma relative clause.

My dad got a new job,and was obliged to change the place of living.

This is a compound sentence made up of two independent clauses --> it can be split into two simple sentences: My dad got a new job. He was/My dad was obliged to change the place of living.

If omitting the pronoun is not confusing and it is clear who/what the subject of each independent clause is, you can omit the pronoun.

Could you tell me which answer in this is and why:

My brother graduated in mathematics last year.He is trying to find ..... in a primary school.
A proffession B job C work D occupation

I seems to me that job is a correct one, but key says the work is correct.How can we distinguish them?

it's work that is only uncountable of the four, and as you can see, there's no article following find, so that was the cue

I saw this translation in one of tests on the Internet

Tom (może nie chciał) to hurt his mum’s feelings but he did. He should apologize
now.

I think that answer should be maybe didn't want,but it is incorrect.Why?

may/might not have wanted

But why maybe cannot be used here?

maybe normally takes a front position in the sentence, before the subject, and not between the subject and verb

w odpowiedzi mozliwe, ze bedzie might not have meant

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