Learn German: Die Villa hätte einen großen Pool. - The villa would have a large pool.

hätte is the special Subjunctive II (Konjunktiv II) form of haben. While you usually build "would" sentences by using würde plus an infinitive verb (like würde spielen for "would play"), haben and sein are exceptions. They are so common that Germans almost always use their single-word forms instead: hätte (would have) and wäre (would be).

Why is it einen großen Pool and not ein großer Pool?

Just like the normal verb haben (to have), the imaginary form hätte (would have) requires a direct object, which means we must use the accusative case. Because Pool is a masculine noun (der Pool), the word for "a" changes to einen, and the adjective groß takes the matching -en ending to become großen.

Is Pool just the English word? How do we know its gender in German?

Yes, Pool is a loanword borrowed directly from English! While there is no strict rule for the gender of all English loanwords, many of them default to masculine in German, making it der Pool. Just remember that because it acts as a noun in German, you must capitalize it.

How would this sentence change if we were talking about multiple villas?