First person:
The main concern isn't the age difference (3 years is negligible. I can't name you a single girl in my high school whose boyfriend was younger than 21) but the fact that she lied. On the other hand, you do say you would have stopped talking to her if you had known the truth, so obviously she wasn't paranoid here.
It's true that online people might be lying about more. She might actually be 14. She might actually be a guy. She might be anything. I find the best way to tell is to see someone's ID. Don't ask her to scan it and send it to you though, it's creepy... Unless you're willing to send yours first, knowing that it's a risk.
I always get guys' IDs on our first date/meeting (always in a public place with people knowing where you are, possibly even people in the area to stand as witnesses. Same for her. Suggest she comes with a friend or family member, sure it will be awkward but that's protecting both of you guys). You can just say you wanna trade pictures or something. People have always been fine with that with me, you trade IDs, laugh at each other's pictures, check that their name and age match what they've told you and return the thing.
If she's actually 17 and you live in one of the rare places where it's still underage, don't have sex with her, but hey, you can still be friends, at the very least online and possibly in real life. As long as you meet her in a public place, as I said, for instance a restaurant, and that you leave separately, you should be fine. Use that date to see if she's immature like Lara suggests or not.
Of course to really know someone you need to live with them and share your everyday life, but you can get an idea by talking with them at least. When I was 23 I followed a course and there was a 17 year old and a 14 year old there, and we were friends, and we saw each other outside and stuff. I also had older friends when I was the one that age. There is no reason you can't be friends with someone who's younger than you if you do nothing inappropriate. Honestly, the "she's too young, to have sex, should I cut all contact?" think reeks of "tits or GTFO" to me. She can still be your friend even if you never ever date, dude. Just don't talk about sex and keep your IM records in case someone ever accuses you of inappropriate behaviour.
I would normally suggest talking on Skype and the like to get to know each other better... you still can (and if she refuses it might be a sign that she's a guy, for instance) but then I'd avoid video. If she's underage and flashes you for instance you could get in trouble, depending on the law. Which is a shame because it would be a way to check she's really who she says she is (the video, not the flashing).
Second person:
So you like them big. Nothing wrong with that. I'm going to assume you're still young? Dan Savage has mentioned more than once that guys often went to him saying that they liked big girls but ended up dating not girls they were attracted to, but girls they thought their pals would find attractive. They were miserable and so were the girls.
While apparently after college people start being more comfortable with being who they are and not who they think their friends want them to be, there are still guys who marry skinny chicks they're absolutely not attracted to. Don't let that happen to you. Appearance might not be everything, but if you plan on being sexually active you need to be able to look at her and find her appealing.
It's hard to own up to who you are when it's not the norm. People might laugh at you. Then again, they might also not.
If you love someone and she's the most beautiful person ever for you, you don't want to disrespect her by pretending she isn't just so people don't make fun of you. Don't do that. It's terrible for the girl it happens to. It's like gays who date people who are in the closet. On the one hand they rush to them for sexual and emotional gratification, on the other hand they insult them in public.
You need to stand up for who you are, and people will get used to it. Sure, you might be the "fat lover" or something but you can still carry that like a title and not an insult, because after all, that IS what you are, and there is nothing wrong with that.
