If you're a US citizen you need the form you linked to. As far as your invitation is concerned, you can't just go to Russia. You need to be invited. You can get an invitation for $20 or so from one of the visa processing agencies. The resultant document will assure the government that you have reserved and paid for your hotel, tours, etc. Of course, you never intend to go to said hotel, etc. and they are not expecting you to show up. Everyone knows this, but you need the document to get a visa. That is how the game is played.