Translation:Waiters pick up the plates from the tables.
I'd say that a plate is just the thing on which you eat, but a dish can also mean the meal that's on it.
Also, a dish often means something like a plate with a high rim, but not quite as high as a bowl.
Two consecutive consonants in word that follows „z” make it hard to pronounce. That's why we add -e.. We do similar thing with: w(e) and rarely (exceptionally rarely) with:
bez(e) - usually always „bez”, except when: beze mnie
pod(e) - same as before: pode mnie
nad(e) - nearly the same: nade mnie, nad/nade wszystko and maybe few more
przez(e) - as before: przeze mnie
spod(e) - as before: spode mnie
"pod/pode drzwiami", "pod/pode drzewem/drzewami", in older writings "pode dwór"
"przezeń" sometimes used instead "przez niego" (because of him; by him)
"spode łba/łbów", "spod/spode drzwi"; sometimes "spodeń" used instead "spod niego"