I would say :"说/讲屁话" / "说/讲废话" / "在酸他"
屁话 is literally translates to "fart words", XD and is normally used when someone says something bad / rude / when you know someone well that when you say this they won't get offended.
废话 translates to useless words / may translate to trash talking (废 also means waste) and you can use it when someone says something that is obvious, or says something that is idiotic. In my country (Malaysia), we used to say 废话 when our friends are chatting about nonsense / stupid / not important / trivial matters. Talking gibberish if you'd prefer.
吹牛could be boasting.
For the story you can say the American 在酸那个华人, 酸 meaning sour -> to verbally pull one down in a sarcastic way because of their failure / weaknesses. Don't be that acidic guy.
I would say 一点都不靠近 for not even close, but it would sound weird ,long and awkward (you're supposed to be the cool winning guy but then suddenly say too much and it doesn't seem cool anymore.)
差得远would be better , since it's short and smooth, but it means long difference ( literall translation).
*I use simplified chinese and I use Malaysian style chinese