Receivers doesn't matter, tuners do. And a basic SWM system will accommodate 8 tuners (hence the name SWM8 - where as a SWM16 would support 16 tuners).
So it depends on what receivers you are putting in. A Genie (HR34, HR44, HR54) has 5 tuners in it - client boxes (C31, C41, etc.) do not take any tuners at all. Regular HD DVR (HR24, HR23, etc.) take 2 tuners. And regular HD boxes (H25, H24, etc.) take 1 tuner.

Once the signal leaves the SWM8 switch, it just like a cable TV feed. You can split it however you like. But you have to calculate your losses. You could run the feed into an 8 way splitter, then 1 output of that into another 8 way splitter, then to a receiver. It will work depending on signal loss in the rest of the system but that is usually stretching it.
Best to use the smallest splitters you need to get the job done. Just like in cable TV.

Also: Why not use a SWM LNB and do away with a switch entirely?
Also (2): I would recommend running the power down it's own coax to the SWM8 switch. If the power supply has to go at a receiver, do NOT put it with the Genie. I can't tell you how many times I have had to fix a system because the power supply will not pass all frequencies properly to a Genie (which uses 5 tuners).