1)Well answered already. Maybe they also could close off the shaft somehow. Also, caves can drain naturally. And the Romans used stone for carrying water, I'd imagine the Dwarves could make gutters to the Anduin, the lakes, and the water table.
2)Gandalf has his very strange ways.
3)And hence also a weak defense point being cut off from any rescue or recent supplies. In theory it seems a firm defense though as it showed folly. It did work I imagine in that it prevented desecration of the tomb for a prolonged period of time and more likely to be skipped over during a quick pillage or descration parry.
4)More exits seem nice, but only a few more. They had been fighting Morgoth for a prolong period and wouldn't make it too easy for him to find lots of back way in. There would be an escape tunnel somewhere forgotten. Plus that can go to the top of the mountain if they must. Which is really three right there. I'd imagine they'd find a way out using their shafts given a few months. I'd vote for no more then 6  ways out, total. Natural, perhaps more, albeit not all feasible (unless your a Balrog)
5)Well covered already. It would have been maintained up to the release, and not too much traffic over it would of occured since. Orcs didn't come as often once it was fully plundered. No winds likely, no water likely. No eroding forces unless the Orcs keep coming and going. And a good enough arch should be able to carry much more weight then Orcs without plunder would weigh.

Challenge:

Simple, Dwarves like wealth. They sold the leftovers. Plus there was the tower at the top of Khazad-dum. Shipped it up to Belegost and Nogrod and let them worry about it. Part of the area would of been pre-existing cave structure as Mim suggests.