In addition to what christian said, I believe you can also tell by the way mögen is conjugated.
How do we know its "sister" or "sisters"? There won't be any change in other words if its plural or singular would it?
Not sure what you're asking. The following was already posted above:
So, there clearly is a discernable difference between singular and plural.
Couldn't it also mean "The sisters like my cat (singular)"? Katze is feminine, so it would take "meine" wouldn't it?
"meine Katze" only means "my cat", not "my cats".
meine Katze = my cat
meine Katzen = my cats
Why not to translate it as "love"? Well, moegen = like, lieben = love, but is "love" that wrong in this case?