Similar to the vertical tail on your Cessna, a flying wing produces only little lift or even a downforce over the rear part of its wing. A swept flying wing uses washout for the same effect. In all cases, the idea is to produce relatively more lift increase with an angle of attack increase in the rear parts of the wing (or the tail in conventional configurations) so the aircraft stabilizes itself.
This also means that the center of lift is ahead of the quarter chord point of the wing, and the same goes for the center of mass. At high angle of attack you need to create a pitch-up moment with the elevons in order to trim the high angle, and once the wing stalls, this pitch-up moment is reduced. As a consequence, the flying wing will pitch down and recover. Again, this is very similar to what happens on your Cessna, only that the function of the tail is performed by the rear part of the wing.
Wing sweep helps a lot to pull the aircraft into the wind, and the yaw inertia of the big wing helps to keep rate changes down. Stalling in banking flight produces a very similar reaction as a straight and level stall while the airplane continues to turn. Of course, pulling too hard and preventing the wing from correcting the high angle of attack itself will risk to force the flying wing into a spin.
Flying wings have only a steep spin mode. Flat spins are not possible because the flying wing lacks the lengthwise mass distribution of conventional airplanes which creates a strong pitch-up moment in a spin. If the flying wing has no fuselage protruding in front, it also lacks the stabilizing nose vortices which are a contributing factor for flat spins.
Spinning the SB-13 was quite harrowing: The nose points almost straight down and the aircraft loses about 100 m in one turn. But ending the spin was simple: Just pitch down and stop the rolling motion by allowing the roll damping of the wing to kick in.