This reminds me of the mini pie dilemma scene from a movie. I forgot the title.
There are three pies: 1x lemon, and 2x raspberry.
There are three mouths to feed: Ann loves lemon, John loves raspberry, and Steve has diabetes. They don't know each others' tastes.
However, politeness dictates Ann choose first because she's the guest. She wants lemon, but if she picks it, there will only be 2x raspberry left, so the others won't have a choice, and she doesn't know what they like. So in order to be polite and allow the others a choice, she picks raspberry.
One of each type of pie remains. Steve is also a guest, so he chooses next. He picks raspberry because lemon is just too sweet, and he'll only eat 1/4 of the minipie (not eating it would be rude to the one who purchased the minipies, but he has to mind his blood sugar!).
John is left with lemon which he hates. Everyone says the pies are delicious and exchanges polite compliments while staring at the others' plates in envy.
The problem here was they didn't have enough information to reach the best decision, and no-one took the initiative to fix it, resulting in an absurd outcome.
When the food came, I got it, and Alice didn't.
Here (France) the waiter would serve the girl first and you'd be expected to be chivalrous and keep your stomach in check, although that chivalrous tradition is kinda lost now. I wonder if it's the same where you are, or not?
I proposed splitting 50:50 between the two of us (we were both extremely hungry)
You took it upon yourself to solve the problem (good) but when you do that you also accept responsibility if it goes wrong...
Alice, frowned and got up. She wanted the whole thing (as I later found out). She wasn't interested in sharing...
Perhaps the misunderstanding here was that etiquette would dictate Alice gets the plate, and she knew it, and you didn't. In this case your actions could be perceived as rude, although it wasn't intentional. Since this is very culturally dependent, you be the judge.
However, she didn't say that. She could have teased you a little bit, say "come on, ladies first", stuff like that, but she chose to leave the table instead. In this case don't fret it: it's now her problem. You don't have to apologize for someone else's childish behavior. Unless you somehow broke etiquette from your culture, but I can't say.
later, she mocked me saying I eat a lot (bhukkad in Hindi) and said that I chew too loud, and I clang my silverware, and many rude things about my eating habits.
Of course! She was a little bit miffed, so she gave you a good ribbing and teasing in return. Fair enough. Don't take it literally, and especially don't get angry at her, that would be a bad move. The "incident" was pretty much a non-issue, there's no need to escalate. You can (and should) even tease her back a little bit.
Her parents were angry at me too :(
How can I avoid this from happening again?
You can ask her parents what you did wrong, and frame it like you're trying to improve your table manners. Perhaps they will give you useful information. If they convince you that you did break etiquette, then you can apologize, but not too profusely. I mean, you didn't run over her hamster with your monster truck or anything, it was mostly a non-event so no need to overdo it.
Also remember the lemon pies, and when you feel an absurd situation brewing, don't be afraid to be the one to open your mouth.
Now, there is an alternate explanation for her behavior: she might be attracted to you.