"The butterflies in the zoo are his."
Translation:Le farfalle nello zoo sono le sue.
Simply put, you don't; there's hardly any need to distinguish when speaking of a third person, and gender isn't the most convenient attribute to identify a person anyway (around half the world has the same gender). On the other hand Lei is also a courtesy pronoun, and the distinction between his/hers and yours is much more sensible; in writing you can capitalize to distinguish, but in speech it can be really ambiguous.
The possessive matches what it refers to (the owned object), and in this case it refers to the subject; it's semantically not that different from "sono le sue farfalle" (it is syntactically though). As a side note, the article is optional when the possessive is a predicate, i.e. it could have been "le farfalle sono sue" as well.
The verb is always conjugated in accordance with the subject: "la farfalla è ..." (the butterfly is ...), "le farfalle sono..." (the butterflies are ...). Note that the subject doesn't necessarily come first, and that when using a past participle it doesn't always follow the same rule.
No, it has nothing to do with butterflies being plural or pasta being singular, but everything with the next word. It is "nello" instead of "nel" because "zoo" starts with a "z": "lo zoo". "in + lo"="nello"; "in + il"="nel". You can read more about this subject in the Tips and Notes of chapter Basics 2.
It's an open door, but don't think of learning a language as a competition. Everyone learns at their own pace. Some people have already progressed because they have been busy for some time. Others because they can and want to spend more time learning. For other people, learning takes almost no effort because they have a talent for languages.
At school I had tremendous difficulties with German and French; I was glad I didn't have to take an exam in those subjects. English was also difficult for me (especially the pronunciation and place of the adverb, place and time), but that language was a compulsory course. Now that I learn with Duolingo, it turns out that I can learn languages, that I have remembered a lot from the past, and that I enjoy learning.
Some languages suit you better than others. I am currently mainly working on Swedish and Norwegian. I see that you have also learned some Romanian. I have known someone who spoke several languages fluently. When he started learning Romanian, he found it the most difficult language he had ever come across. So be proud of yourself for learning other languages. Do it at your own pace and enjoy it. And don't worry about people who get a lot of points, although it is nice to stay in the league ;-)