This is what I have figured out for the quests so far:
1st quest) You just pick up money on the ground. It's located mostly on the right part of the town, and they are tiny little grey dots. You'll see them. Once you get like 4 or so, the main character talks and then you complete the quest.
2nd quest) This requires you to move boxes. I'm not sure if you just move one or all of them, I did all of them to be thorough. You can pick them up and drop them with a. You can do this with moving NPC too, but I haven't noticed any effect.
3rd quest) Pretty straight forward. Just go to the sewer and get water from the water fall in the bottom left. Might need to get a few levels to more easily walk through here, as the enemies kick your butt.
4th quest) This unlocks leaving town. Just to the north is a hill and you need to collect 5 herbs and 5 jars. These are items on the ground you pick up, but they look like the scenery. The jars use a flower sprite and the herbs just look like weeds. Again, enemies ramp up again, and at night they have stronger variant.
5th quest) Go to the graveyard at night (sleep in bed, second option) and go to the question mark. A ghost will appear. I was level 9 when I fought it and I decimated it, so I wouldn't be super worried about your level.
