Is there any indication of female subject here?
Yes, बिल्लियाँ (cats) is feminine in Hindi, that's the subject. Whether you say "His cats" or "Her cats," (same sentence in Hindi) the subject is still "cats," it doesn't matter who they are owned by.
And उसकी just depends on the noun that comes after it, it doesn't matter whether the person who owns it is male or female, if the thing they own is feminine it will always be उसकी.
Since उसकी refers to the cats, how do we know the gender of who owns the cats. Can it be either: his cats and/or her cats.
Yes, both are correct translations, you would just go off of context to understand which is meant.