1. You can not use the Visual Studio Publish feature to build a correct package for mojoPortal. I make packages with the free UnleashIt tool.
2.You can't only build thw Web project, you must build the whole solution. Then visit the setup page.
3. I don't know what you mean about restored a new database. Only existing databases get restored from backup not new ones so I have no understanding of the condition of your db.