I know what you mean about uploading pics, it can be frustrating. Obviously you have some plumbing repairs to do, it's conceivable that the burst hose could have let go due to age (which means others will have to be changed as well), but my guess is that a connection has failed, possibly the bottom one you mentioned. As to the fan spinning freely, I think it should do so, with very slight resistance; if it's freewheeling, I think that would mean the water pump is shot.
I wish I could be more definitive, again my guess is that you're in for radiator, thermostat, and hose replacment, and complete flush of the cooling system (kinda goes without saying). If you shop around, my guess (and it's largely a guess) is that you're in for $300-$500 in parts, maybe nearly double that if you have to throw in labor. If you caught the overheating quickly enough, there may be no harm done to the engine, but short of more dismantling of the engine, I think you just have to wait and see what happens once you put things back together and start driving around.