Tried sleeping in a bed but couldn't find a way to do it.

Basicly it's night time and all the houses are closed but I need to go to the store to continue.

Any way to speed up time from night to day?

Eventually, yes, you acquire a magic bottle which can speed up time. Before you get that, though, you just have to wait outside. Time doesn't normally pass indoors, so just go outside and for a few minutes.

Not very far but that's probably my single biggest complaint of the game, there isn't really enough to do that forcing us to simply wait is a good design decision.

Other than that, it seems pretty cool thus far.

EDIT: I may have misunderstood, I thought I needed it to be a specific time to allow me to do something but I was wrong.