Learn Hardcore Korean: gwaireul yeoseos gae sasseoyo.

Korean often omits the subject when it’s clear from context.
So 과일을 여섯 개 샀어요 can mean I bought six fruits, we bought six fruits, etc., depending on the situation. If you want to specify, you can add:

저는 과일을 여섯 개 샀어요. (As for me, I bought six fruits.)
제가 과일을 여섯 개 샀어요. (I (specifically) bought six fruits.)

What does 을 do in 과일을?

을/를 is the object particle. It marks 과일 as the direct object of the verb 사다 (to buy).

과일을 샀어요 = (someone) bought fruit(s)

In casual speech, it can be dropped sometimes (especially in conversation), but keeping it is standard and clear.

Why is 여섯 개 used instead of just 여섯?

Korean typically uses a counter when counting nouns.

여섯 = six (number)
개 = a general counter for items/things
So 여섯 개 = six (items).

Without a counter, the sentence sounds incomplete or unnatural in most everyday contexts.

Why is the counter 개 used here? Are there other counters for fruit?