Is 'reszty' mean 'the rest' as in 'the remainder'?
Yes. It can also mean 'change' when talking about money returned to you when you pay for something (e.g. in a shop).
Why can't I translate this to "we are not seeing the rest"?
The occasions when the word "to see" uses Continous aspect are rather rare, that shouldn't work here.
Can it all mean 'the change'
You mean, like, at a check-out? Says so above (2 years ago).
"remainder" not accepted in this sentence, although it is allowed in other similar sentences....
Is the pronunciation correct? It sounds like "rerty" and when I click the word, the pronunciation sounds different (and correct)
The sounds seem okay, although there is something weird in the pronunciation at this point that you mention. Anyway, it's supposed to be sz.
Why not a rest
I think that "reszta" as "remainder" needs "the".
If you mean the verb, I think that type of rest is a different word in polish - odpoczynku.
The basic form is "odpoczynek" then :) But in this sentence it would be "odpoczynku", true. However, that interpretation seems rather unlikely in this sentence.