I believe that those vouchers can serve as your invitation. IMHO it's better to pay $20 and pad the dates of your stay in case your plans change. If your visa expires you can not leave Russia without getting another one. Also, you can not stay in a hotel without a valid visa. I've used
www.russia-visa.com a few times. It was (and from what I can tell still is) the cheapest place. I have no idea at all about your legal issue.