To answer your specific questions, you shouldn't assume spring angle is 45 degrees. Put a framing square on the flats of the crown and you'll know if it's symmetrical or 38/52.
To cut this flat, your bevel and miter angles are somewhere in the 30 degree range. See the link below to figure the actual numbers.
Since your saw doesn't flop both ways, you might consider building a mini sled that holds the crown upside down at its spring angle (45 or whatever). Then the only angle you need to worry about is the ~45 inside and outsides. See tutorial on crown angles
(I'm not saying you need to do this; it's just that only cutting crown with only one direction of bevel will force you to cut upside down occasionally, which is bad for tearout and relatively confusing sometimes.)
Mini sled... mine:
(Not shown: the upright of the sled is bolted to the fence of the saw so it won't move. Clamps might be an option, but they'll probably get in the way.
Terrible picture angle, but set the crown upside down with the flats aligned with the base and the fence:
Note the pencil line that indicates where the crown is supposed to sit on the base. Hole in the base so I can see my miter angles.
Finally, tack a straight bit of something onto the pencil line on the sled to keep the crown from slipping out of angle:
Last notes, if you're meeting up to an existing piece, they may have felt forced to tweak the spring angle just a teensy bit, which will make it hard to match perfectly. Do as much as you can to have extra length while you're whittling away at a perfect fit. Don't expect corners to be perfect 90 degrees, either. If it's paint grade, there's a lot of forgiveness to be found in sandpaper and spackle.