YES, the sunhood can be folded up.
I can't give it top marks for the usability of the touchscreen. You have to stretch your index finger all the way out to just reach the touchscreen - and I have rather large hands. On the other hand, the sunlight is blocked well by the "high" walls. This is probably an unavoidable compromise.
Yop, it folds up and takes up almost no space during transport. However, I never used it during the op, so I can't say anything about its usability with the protection.