Actually, It depends on the context. For example:
"My younger brother = meu irmão mais novo" but you could also say "meu irmão menor (as in English "my little brother")."
"My older brother = meu irmão mais velho" and you could also say "Meu irmão maior" (in English "my big brother". It's very common when you're asked about their ages. For example:
Quantos anos têm seus irmãos? / How old are your brothers (siblings)?
O maior (mais velho) tem 18 e o menor (mais novo) tem 10 / The oldest is 18yo and the youngest is 10yo.
Yes, but that is not the exact translation. 'Your cat is bigger than my cat' means the same thing as 'Your cat is bigger than mine'. It's just that it's a different construction.
Your cat is bigger than mine = I'm guessing that would be "Seu gato é maior do que meu". Or perhaps, "Seu gato é maior do que o meu".
I'm not a native speaker, though, so I'm not 100% positive.
If it was a feminine noun, would it be "da que" instead of "do que"?