Jarvan is royalty and has been raised as such from birth, people coming up and kissing his feet is probably not that unusual, so the same could be said of the queen. It would be an unusual thing for Quinn, certainly, seeing as she has not always been royalty so that kind of action and praise would confuse her.
Yes, Quinn would probably try to move her foot, especially if he stayed at her feet for more than just a few seconds.
The size/age of the person does not matter. They want to treat every one with respect; this man ran up to them to praise them and kiss their feet, so he's probably a loyal (albiet a bit fanatical) citizen. They have no need to try to harm him, but they do want him out of the way because he's causing a bit of a scene.
And I'm guessing you mean to say that Jarvan would get jealous over this guy touching Quinn? Sorry, but no. Again, this guy is kissing her feet, not her lips, not her chest, her legs, her crotch. He has no reason to get defensive over that. Kissing someone's feet is an act of devotion and worship, not sexual in anyway. The only things Jarvan would have to be upset about is that his guards let this guy get past them - he could have been an assassin, after all, and their failure could have costed their lives. And the fact that his speech had been interrupted. Quinn's foot being grabbed and held onto would cause some concern, but nothing that wouldn't warrant more than shouting for the guards.