The actual power draw from the fan is not going to effect much, however, a higher fan speed will transfer cold air into the cabin (if the AC is running) more rapidly, and thus require the compressor to be engaged longer (in exchange for more cooling).

Not directly. Though when running AC, it is wise to use recirc, as it can keep the cold air inside the car longer, and actually cool the already cool cabin air further. It doesn't make sense to keep reintroducing hot air from outside. However, if AC is off, the reverse is true, the window glass will cause solar heating, so you'd end up recirculating hotter air, rather than allowing in cooler air from outside to replace it.

I believe it keeps the engine running more in order to run the bigger, belt-driven compressor, rather than switching to the elecrtic compressor. This is the opposite of ECO mode (engine off as much as possible)