At this point, by assigning ground level as minus 1.2m, you've effectively said upwards is positive. Good! Doesn't matter which way round you do it, just as long as you are consistent throughout your working.
Acceleration is negative because it's in the opposite direction to upwards which you've assigned as positive.
Initial velocity positive - yep.
Velocity is decreasing throughout the motion. When it hits the ground it's speed will be greater than the initial speed, but the velocity will be less (it will be greater in magnitude (in this case), but it's actual value will be less, in the same sense that -20 is less than 4, for example).
Accleration does not increase - it is constant throughout.
The suvat model ignores air resistance, and assumes acceleration is constant.
You get two values +/- 7.75 m/s. If you were to draw a graph of velocity against time, then the positive 7.75 m/s value would occur at some theoretical time before t=0, and so isn't valid.
Actual velocity is minus 7.75, if you take upwards as positive.
Yes. Spot on.