So can I run this put back together without Parts #13 and #14 until I get down to the store?
I wouldn't. Without the spring the parts are going to be kinda floating around in there. But, you do not need any of the hub parts to drive it as long as you are in 2wd.
As long as the wheel bearings are in place, it will run just fine. You could carefully stuff some paper towels in there being careful not to get them in the bearings, and drive it.
The best way, though it might be tricky, would be to put the plate with the screw holes for the cover in place with the lock ring.
Then you could carefully put the cover on with the screws. The tricky part would be making sure that you got one of the screws started without pushing the ring back into the hub.
Without all the innards, there is nothing holding it. Once you got one started, it could not go anywhere.
The center plastic piece in the cover would not be held in by the spring pressure either, but the O ring would probably hold it .
As long as you did not do a lot of driving, it should be fine
If you knew anyone who had the blank covers for the use with a chunk, you could just put one of those on.
Heck, you could duct tape a plastic bag over the hub to get you to the store and back.........