To help visualize what others have already explained here's a discharge curve for alkaline chemistry batteries:

Shorting the battery terminals is a curve far worst that the 545mA you see above, so it will be almost a straight line down; how well the battery recovers depends on how much electrolyte was expended. Generally, as the curves show, the useful life of this battery, even if it did recover, is far reduced. The reason why such batteries can recover is the internal resistance is often high enough to prevent all the cells to expending electrolyte to ~ zero, but it also prevents potential injury, such as if you did this with a NiMH or Li cell with known low internal resistances that can explode or get white hot.
To repeat what others have already said on the second question, the AC-DC supply you measured is open circuit, non-load voltage. In poorly or unregulated supplies, they are used for a designed load, the output will appear to be high until the right load is placed. If the supply now fails to function its because its either damaged or its overload or short circuit protection has tripped. The only hopeful news is some supplies have self resetting protection, all you need do is wait and it should reset itself if it has no visible reset buttons. If it has an internal fuse or equivalent, you'll have to open the unit to find and replace it.
Good luck!