To answer your question about the comma: No, there shouldn't be a comma after the "and". Unless it's something like this: Did you see those people giving us the finger? And, right after that, the counter protest? The right after that phrase has optional commas offsetting it. It might have been said with two noticeable pauses, which would ask for commas, or without pauses, which would make the commas wrong for the dialog but not ungrammatical.
I don't know when you were a kid, but I was a kid in the 1950s and learned the same thing: Never start a sentence with "and", "but", or "or". This is still a good rule of thumb for formal written English: dissertations and articles to be published in academic journals. However, very few native speakers pay attention to it any more. I surely don't. And why should I? When I write informal prose, I want it to sound much more like speech than like a learned treatise. Writing like you speak has certain advantages and disadvantages.
I think that the addendum about adding the comma after the conjunction is apocryphal. I've never heard about it from my fellow cartelliards. Most members of the English Cartel (be careful about making sure that "C" is a majuscule and not a minuscule or one of our operatives will be around to cut your left little finger off). But back to the topic.
All writing rules are merely suggestions unless you're forced to use a style manual by your publisher, whether that be a journal or book or newspaper publisher, a high school or university teacher, or some other institution. Grammaticality is not necessarily the hallmark of good writing, and it's not sufficient to ensure good writing.
Bill Withers: Ain't No Sunshine
Ain't no sunshine when she's gone
It's not warm when she's away.
Ain't no sunshine when she's gone
And she's always gone too long
Anytime she goes away.
Wonder this time where she's gone
Wonder if she's gone to stay
Ain't no sunshine when she's gone
And this house just ain't no home
Anytime she goes away.
And I know, I know, I know, I know,
I know, I know, I know, I know, I know,
I know, I know, I know, I know, I know,
I know, I know, I know, I know, I know,
I know, I know, I know, I know, I know