there are a few dialogues with Mary outside, the Angry Neighbour complaining about Max and the hole in the fence, Darnells dog shitting on your lawn, and I think maybe one more that I can't remember right now, there is a Mary Sprite that hangs out there for the entire game, most of the time it is worthless to talk to her there unless you see her with someone else.
I think the quest that unlocks the store might be Mary's weight loss chain, which starts after you play with her food... check the fridge.
But most quests in this version appear way before you can do anything about them, just keep doing other quests until they spawn the triggers you need.