Learn Italian: C'era qualcuno in casa ieri sera? - Was there someone in the house last night?

C'era means "there was". It combines ci (there) and era (was), dropping the "i" before the vowel. If you just used era, the sentence would mean "Was he someone in the house?" instead of "Was there someone in the house?"

Why do we use the imperfetto tense (c'era) here instead of the passato prossimo (c'è stato)?

The imperfetto is perfect for setting the scene or describing an ongoing state in the past. By asking C'era qualcuno, you are asking about the general situation (was anyone present at that time?) rather than a single, completed action.

Why does the sentence say in casa instead of nella casa?

In casa is a common fixed phrase that translates to "at home" or generally "in the house". You would use nella casa (in the + house) only if you were referring to a very specific, previously mentioned physical building.

I thought "night" was notte. Why use ieri sera for "last night"?

In Italian, sera (evening) covers the time from late afternoon until you go to bed. Italians almost always use ieri sera (literally "yesterday evening") for what English speakers normally call "last night". Notte is generally reserved for the deep night when people are asleep.