The play doesn't actually tell us how old Katharina is: though we know for certain that she's older than Bianca. She's been played as everything from a young woman (aged around 25) right the way through to someone just about to be past child-bearing age (so 40-5) - at least, in the Elizabethans' mind!
The play is set in Padua in Italy, so - assuming (and it's not an assumption you can really make, I'm afraid) that Shakespeare intends his play to be a realistic presentation of Padua - you can probably say that Katharina, born and bred in Padua, would be Catholic. Italy is, after all, the seat of Roman Catholicism.
One of the funny things about Shakespeare though is that it's very very rare for him to provide the sort of biographical facts that you're talking about: testament, I suppose, to the strength of his characterisation that audiences down the years have managed to "see" them without concrete details.