At its most basic level
Rear tyres are often thinner with less knobbles to decrease rolling resistance while wider more aggressive fronts are used to improve cornering.
Even with matched tyres it's common to run the front at a lower pressure to the rear.
Yes - they will gum up.
Maybe. Maybe not. I've been on Panasonic Cinder Cross all season - which is a pretty similar tread to the Cross Boss.
A rocket Ron front and racing ralph rear would be pretty good all year round too I reckon.