Sir, that was when it was used as possessive pronoun, like "ihre Katze" (her/their cat) and "Ihre Katze" (your cat; in polite manner). when it is first word of sentence you can't distinguish except by context.
if not used as possessive, on its own, "ihr", does mean "you", but in a familiar plural term of "du".
hope that was clarifying enough :)
Mögt ihr schwarze Katzen? is correct!
It must be ".. Schwarze Katzen" because you have no article before the accusative subject. In the case a DEFINITE article is included you must say "Ihr mögt DIE schwarzEN Katzen".
With an INDEFINITE article you have for exemple "Ich möchte EIN schwarzen Hund haben".
I think that much of what you said is correct - it is indeed plural with strong inflection. However, that means that it becomes "schwarze" for the accusative case (which is the same as feminine)! https://en.wikipedia.org/wiki/German_adjectives#Strong_inflection
This one was tricky for me, so I'll post what I found out here for the future students. mögen is an irregular verb, and in this sentence the subject is in the plural The translation is "you like" but since it's plural, i believe it could also be "you all like" Correct me if I'm wrong.