Did they ever laugh at or mock him for his height?
Yes.
Fiona: And what of my groom-to-be? Lord Farquaad? What’s he like?
Shrek: Well, let me put it this way, princess.
(Shrek dumps Fiona to the ground unceremoniously and heads to a nearby pond to wash up)
Shrek: Men of Farquaad’s stature are in…“short” supply.
(he chuckles and Donkey joins in)
Donkey: I don’t know, Shrek. There are those who think…“little” of him.
(They laugh even harder)
Fiona: Stop it. Stop it, both of you. You’re just jealous that you can never measure up to a great ruler like Lord Farquaad.
Shrek: Yeah, well, maybe you’re right, princess. But I’ll let you do the…“measuring”…when you see him tomorrow.
In fairness, Shrek is supposed to be a thin-skinned asshole in the first movie, too. One of the other big themes of the first films is “Power makes you an asshole”. Farquaad has enormous political power, but Shrek has substantial physical power. That’s what brings them into conflict, and that’s what drives Fiona away from them both before the end of the movie.