Question 1 -
She is very poor, but she does not complain
Answer - "Inspite of....." her being poor, she does not complain.

Question 2 -
The ship went down, yet the passengers were saved.
Answer - "Inspite of ...." the ship going down, the passengers were saved.

Are they alright or there are any better alternatives?
In spite of is three words. I wouldn't use it in your sentences. My suggestions:

Even though she is poor, she doesn't complain.
Even though the ship sank, the passengers were saved.

Students: Are you brave enough to let our tutors analyse your pronunciation?
Sorry, i did not mention that we have to start from "Inspite of..." in this question.

In spite of the sinking of the ship, the passengers were saved.

Sounds better?

In spite of being the ship went down the passengers were saved
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1. In spite of being poor, she does not complain.

2. In spite of the ship having gone down, the passengers were saved.