Yes, you’re right. If it’s your own pet or you happen to know the gender, you would generally use it. It's used like this everywhere. “This is my cat. She is really beautiful.” “That’s my friend’s cat. He’s really sweet.” You would use ‘it’ if you didn’t know whether it was male or female “There’s a dog over there. It looks very playful!” You could also use ‘it’ if for some reason you didn’t like that particular animal. This emphasises your dislike. “We’ve got a cat at home. It’s a horrible little thing, but the kids adore it for some reason.” Some people who generally don't like animals often just use 'it', although it doesn't sound very nice. “I don’t like dogs, but my brother’s got one. I don’t mind it actually because it tends to keep away from me.”

Yes you can. Pronouns "he" and "she" aren't used only in America when it comes to pets that you are kind of close with. It's used in every English-speaking country.

Sure. One would usually start off by introducing their pet and the pet's name and then you can go on to refer to the pet as he or she. Note that when you refer to an animal with he or she the animal needs to have some significance, or be well known, you wouldn't refer to a random male dog on the street as he. Example: I have a cat named Lucy. She is very cute.

Yes, we call an animal 'he' or 'she' if we know the gender. If you see a beautiful cat, and you know that it's a female cat, you say 'She is beautiful'. Likewise, if you know that it is a male cat, you say 'He is beautiful.' We always refer to pets as 'he' or 'she', and it is also normal to refer to other animals in this way. For example, a racehorse, a guard dog or a subject on a wildlife documentary would also usually be referred to as 'he' or 'she'. Note that we can't say 'This cat he is beautiful.' because this is not grammatically possible. You can say 'This cat is beautiful' or 'He is beautiful' or 'She is beautiful'. You cannot have both 'This cat' and 'He' or 'She' in your sentence. Whoever taught you English has misled you about two things: 1. It isn't true that animals should be referred to as 'it' because they aren't human. In fact, it's very common to use 'he' or 'she'. 2. It isn't true that the USA has different grammar from the rest of the English-speaking world. The grammar rules are the same in all English-speaking countries.