It depends what nationality / citizenship you hold. Generally speaking tourist visa is the easiest, especially if you're American. For the same price as the single/ double entry- one can obtain a 3 year multi-entry tourist visa.
No, you dont need to disclose anything but the cities you are wanting to visit on the invitation letter.
The biggest issue you will face is the registration. You have 7 days to register. In most hotels will do this for you. When staying with the friends, the OWNER of the residence will need to register you. Depending on the local office, they may or may not be able to use Gosuslugi to register. If its not available, both of you will need to go and register at the local office.