Check out www.vcdl.org for most of the information you seek. As for open carry laws, there aren't any specifically addressing this. Virginia doesn't tell you what you can do, she tells you what you cannot do.
Businesses that post a "no guns/no firearms" sign also reserve the right to allow you to carry onto their property if they so desire. However, unless the owner/manager is willing to take such a decision, consider the fact that it is posted means they do not want your business when you are armed. They cannot hold or arrest you but can summon the police and have you charged with trespassing. It is best not to enter such businesses.
INAL so I welcome corrections to what I have offered here.