Why am I seeing stagnant water inside the shower drainage pipe hole?
Yes it's normal and what you want. It's called a P-trap and the water sitting in there seals out the sewer gasses. 

My ASCII P-trap:

                  \ /
                  | |
   __________     | |
   _________ \    / /
            \*\__/*/
             \****/
              ----


The asterisks would be the water that forms the stopper. 

In an empty home or in drains that are infrequently used (such as a basement) you these traps can eventually dry out from evaporation and let sewer gasses seep in. 

In your case, if you aren't going to use the shower for months on end, I suppose you could add a drop of bleach to the drain. If the shower is used semi-regularly, there should be no issues at all.