It could certainly run with 20 staff – it would just spend a lot of money on license fees to a separate Facebook Services Inc that provides software and server administration services. This is similar to how companies avoid tax e.g. IKEA and Starbucks.
It could similarly avoid large profits but avoiding large revenues works be trickier. But I'm not an expert in these things, so maybe it's possible if you really know what you're doing.
The problem is, there's no legal distinction between a company that own shares but is "really" part of the same company, vs a completely separately company owning shares e.g. a pension fund.
It could similarly avoid large profits but avoiding large revenues works be trickier. But I'm not an expert in these things, so maybe it's possible if you really know what you're doing.