"Do you also think that she is a bit stuck-up?"

This is correct, but sounds very formal. Usually if you're talking about someone being stuck-up it's probably an informal conversation so it would be more like:
"Do you also think she's a bit stuck-up?" or "Do you think she's a bit stuck-up too?"

"Thanks for checking up on me, I have indeed been feeling a bit down for the past few days.

This also sounds formal and people are usually not that formal in English, even in formal situations! The word "indeed" is very formal and I don't think it's actually used that often. It is used formally but I think in a sentence like this it wouldn't be. People also don't necessarily say "for the past few days" but just "the past few days" or "lately".
I'd say more like:
"Thanks for checking up on me, I have been feeling a bit down the past few days" or "I have been feeling a bit down lately"

"The ceiling has been shored up with steel girder to prevent that the house collapsesing."

With "prevent" we usually use the -ing form of the following verb, so "to prevent the house collapsing" instead of "to prevent that the house collapses".