No! No! No! Definitely not. Calling a person's baby 'it' is an enormous insult, and the parent would be extremely angry and offended if you did so. Here's how a typical conversation would go: I see a friend with her new baby. I smile with adoration and look closely at the baby, looking for pink frills or flower designs to give me a clue. If I find any, I presume it's a girl and continue accordingly. If not, I continue to smile at the baby, and say: "Oooh, who's this?" If my friend says "This is Sara" or "This is Jack", I'll know if it's a girl or a boy and I'll continue accordingly with the appropriate gendered pronouns. But let's say she says "It's Laurie". Hmmm... that could be either. So I might need to ask another gender-free question. So I look at the baby and say: "Hello, Laurie! How old are you then?" With any luck, the mother will then say "He's five weeks old" . At this point, I'll have had enough of this awkward guessing game, will breathe a silent sigh of relief, say "He's lovely" and the conversation will then go on smoothly without fear of offence. (With all respect to the other respondents, I would guess that I have probably spent more time around parents and babies than they have). By the way, a version of the same conversation happens with pets, albeit without the pink frilly clothes. Pet owners will also be very upset if you call their darling doggy or pussycat 'it'. You also need to avoid using any gendered pronoun until you've found out from the owner whether their pet is male or female. Never use 'it' directly to a parent or pet-owner.

Yes you can but there is a small chance that a few people may, get a little offended by it. If it is obvious that a child or baby is male you should try to ask "what is his name" if it is obvious the child or baby is a female you should ask "what is her name". For dogs and animals you will hear people more often ask "what is it a dog or bitch" and then when you know how the owner prefers to call the pet, you can use that. I have found that in other languages they find this strange to ask "what is it" for enquiring about a pet.

Use 'their' if you don't know the sex. 'It' is not for people. It's technically not wrong I suppose but it sounds super weird.

If you don't know about the gender of the baby, Yes. You can use it.

It is sometimes said by native speakers but is generally considered rude for human babies. For animals, most consider it fine but a few sensitive people will also consider this rude. If you don't know the gender, "their" is becoming more correct and acceptable to use. Some will say it's technically incorrect, but I think it's the best option and is making its way toward "correct" for most English speakers. SuKi's suggestion of "Oh, and who's this?" is a great suggestion.