Unless the quiz setter has changed it since seeing this, the question actually asks what sect Assad's allies are from. Iran, Hezbollah and the Iraqi militias are all Shi'ite.
"What type of war is the Syrian War" is way too open-ended of a question. I tried "civil" and "guerilla," both of which are correct. I never thought of "proxy."
Yes absolutely. It's a good quiz but this is a bad question. I tried those and 'insurgency' and 'regional'. All of them would have been fair descriptions.