Is it true manufacturers, publishers, and record labels restrict merchants from selling items before the official street date? OR does each store (online/brick and mortar) set their own policies?

Yes, record labels, manufacturers and publishers "restrict" release dates. It all has to do with marketing and publicity. It's for the same reason they put release dates for movies in the theaters.

So then stores who sell/ship preorders before the date are in violation? That's what I don't understand. Why do some stores sell/ship before the street date and others do not? Do the companies really enforce the street dates?

Companies do enforce it. I think shipping early isn't a big deal, as long as customers aren't routinely receiving the discs before the street date.

The studios will sometimes give stores less promotional materials if they break street date. So it's not a hugely big deal. They're not often going to hold out on shipping product, as that will just cut into their sales.

The reason I ask this question is because I notice that stores in New York (from where I just returned) almost always have the items the weekend before the street date, but it's rare for a store here in Ohio to sell the items before the street date.

There are some online stores that ship before the ship date, and those that ship on/after the street date. If you're receiving an item on or after the street date, what does it matter if the company ships it before the street date?