Breakdown of Gdyby nie szybka interwencja, mogliśmy stracić dom.
dom
house
nie
no / not
móc
to be able to
szybki
fast
Questions & Answers about Gdyby nie szybka interwencja, mogliśmy stracić dom.
Why is szybka interwencja in the Nominative case? Doesn't the word nie usually require the Genitive?
You are right that nie normally changes a direct object into the Genitive case. However, the phrase gdyby nie (if it weren't for) is a special fixed structure. It always takes the Nominative case, which is why it stays as the basic dictionary form szybka interwencja instead of the Genitive szybkiej interwencji.
Why does the sentence use the past tense mogliśmy instead of the conditional moglibyśmy (we could have)?
In everyday Polish, when a sentence starts with gdyby (which already sets up a hypothetical situation), speakers often drop the conditional particle -by in the second half of the sentence. Using the conditional moglibyśmy is also completely correct and slightly more formal, but the past tense mogliśmy is very common and natural in spoken Polish.
Could I use the imperfective verb tracić instead of the perfective stracić?
In this context, you need the perfective stracić. You are talking about a single, hypothetical completed action (the total loss of the house as a final result), not the ongoing process of losing it.
Can I insert the word to before the second half of the sentence, like saying 'then we could have' in English?