I am only in my second year living in W-S, so here is what I know so far:
To answer ques# 1: It is Billy Bob's Silver Diner. I have never eaten there, so I can't give you first hand info.
About Us - Billy Bob's Silver Diner (broken link)
#2 - The stadium being built is for the Class A Winston-Salem Warthogs, but other events will be held there too. The proposal includes "In addition to a 5,500-seat baseball stadium, the overall development would put a 30-acre village of stores, residences, offices, restaurants and a movie theater between Broad Street, Peters Creek Parkway, Business 40 and Brookstown Avenue."
#3 - Downtown is trying to be revitalized, especially 4th St. You probably saw a lot of people eating outside of Mellow Mushroom. They tend to have the biggest outdoor crowd. I personally like the Foothills Brewery for beer and Mellow Mushroom for pizza and beer. Trade Street is also cool.
#4 I am clueless. Sorry!