Why is the Pirs docking module being discarded?
The head of RKK Energia says Pirs lives longer than 2x of its initial planned resource.
The wonderful ideas like "Save Pirs!" don't seem to be based on solid grounds. MLM has incompatible docking adapters. Even if it had compatible docking adaptors it'd be cheaper to bring there another Pirs than to save the current one with any complex schemes.
For example, one of the (seemingly obvious) ideas, is to use the Progress spacecraft needed to deorbit Pirs to just detach it from ISS, and fly near the station indefinitely until MLM or MLM+UM arrives. Then dock it back using the same Progress. The problem with this solution is that for deorbiting a regular Progress can be used.
While for docking back, it needs to be like
the one that brought Pirs to the ISS. Otherwise the thrusters are too far away from the center of mass for fine maneuvering needed for the docking:
In other words, to keep Pirs afloat that way one needs to spare another customized Progress. And if that's a customized Progress, then there should be some design process to bring it to ISS without Pirs (with some other payload).
Another, (seemingly simpler and even more seemingly obvious) idea is to hold it with Canadarm and dock back when possible. It faces obvious problems of not having the manipulator attachment fixture on Pirs, the manipulator ocuppied indefinitely. And less obvious problems, such as powering Pirs off indefinitely and then back on.
After considering all different scenarios and costs of saving Pirs, it was decided to deorbit the old tin.
(This is rumours though, I can't cite any reliable sources, other than publicly stated deorbiting plans)
Does Zarya have a zenith docking port?
No it doesn't.
It was planned initially, but then the plan has changed and a spherical cover has been placed instead.
See this scheme on the cosmonaut training center site.
Number twenty two says " Пассивный стыковочный агрегат" that is "Passive docking unit".
While number five says "Стыковочно-такелажный узел ERGF для захвата американским манипулятором." that is "ERGF docking and rigging adaptor for American manipulator".
Here you can see it from a better position:
And this is how it works: