"The cat punished the kitten because it kissed the mouse."
Translation:La kato punis la katidon ĉar ĝi kisis la muson.
Sometimes word order does matter, and clauses seem to be universal. The first clause here is " La kato punis la katidon" the word ĉar then separates and ties together that clause from/with the following one: "ĝi kisis la muson." We know that the subject/verb/object of the first clause are the result of the second one because/ĉar…
In other words: if the sentence were to be: Ĉar la muson ĝi kisis, punis la katidon la kato, it might be a bit difficult to parse, especially if you only heard it. But, once you worked past that, you would still see that, because of the clauses, the sense is still there, and it could only be la katidon that is the ĝi after the connecting word (which happens to come first here, because this is one of those words which must come before the words/phrase it modifies).
I hope that didn't turn into word salad. It's really a simple concept, but I was up late last night.
I would argue that the sentence would not change if "it" was referring to the cat. We don't know for certain whether "it" is the cat or the kitten here. The same is true whether you are reading the sentence in English or in Esperanto.
Because "ĝi" is the subject of the clause, there is no accusative applied to it, and this is true regardless of whether it refers to the cat or the kitten.
The suffix ~id denotes the child or offspring of the root. So you may occasionally see words like reĝido (prince/ss), arbido (sapling), Iszraelido (Israelite), Latinidaj lingvoj (Romance languages) and Araĥnidoj (itsy bitsy spiders).
In fact, one of the great efforts to "improve" Esperanto is a language which chose to name itself Ido. (If you've never heard of it, don't worry, it seems to be going the way of Volapuk.)