Odo has absolutely always returned the cart. In fact, I'd say he's tracked down everyone he can find that hasn't returned the cart and forced them to return one in front of him.
Nah, Odo believes in rules and order too much to force others to return their cart when there's no rule saying they need to do so.
He doesn't like it when people leave their carts in random locations, which is why he leaves his very neatly where it's not going to be a danger of rolling into a car or the middle of the lot, but he definitely isn't going to return it himself when it's someone else's job to do so.
Yep, and he'd probably return other people's carts too while grunting about the decay of federation morals and wishing he could put them in the brig for a few hours.
I don't think he would put other people's carts away.
He would track them down and make them do it themselves.
While grumbling about the decay of federation morals...
And obviously he put them in the brig while going over all laws and regulations to figure out if he can lock them up. He does that every time. It would be improper not to double check.
Also he will arrest Jake and Nog and drag them into detention for Nog's quarter scheme. Quark will feign being outraged but then will insist he be included next time so he can teach Nog how to not get caught.