Bending stresses may be harder to calculate, but they will be much higher than for sawn (or hewn) sections. The second moment of area can be easily calculated, but I don't know where you'd get the Young's modulus values.

The allowable deflection would depend on your plans. L/200 to L/400 are all values that I've seen thrown around. If the beam is not supporting a finished (plasterboard) surface and you can tolerate some movement then you could comfortably go with L/200 or even less.

As Jay says, you do have a potential degradation problem. While both Douglas and Red Cedar are rot / insect resistant, this applies only to the heartwood. And since you're incorporating the sapwood into the joints you'd need to be sure that if the sapwood was attacked, the remaining heartwood - heartwood connections would remain resilient. To my mind this would mean cutting shoulders through the sapwood to ensure that load doesn't end up on the pegs when a wood borer munches it's way through the outer 4cm of your trees!

3. I was asking similar questions not that long ago. Mortise and tenon joints with scribed shoulders to mate the round exterieurs of the timbers. Have a hunt on youtube. Or buy Ben Law's book.