"The woman pays us."
Translation:Η γυναίκα μάς πληρώνει.
In speech, the possessive is a clitic -- it has no accent of its own and is essentially pronounced as a part of the preceding word.
So the difference would be something like iyineka mas plironi in the first case, iyinekamas plironi in the second case -- the second one has the mas joined up into one word with the yineka from the point of view of word stress.
It could be OK in spoken Greek meaning "it is the woman paying us" (not someone else), or something like "she is paying us - not taking from us", therefore I wouldn't say it is the exact translation of the given phrase as it all depends on the emphasis put and not the standard structure to be taught.
No! The weak form μας goes before the verb. The strong form εμάς is used after it. It is valid for other cases of the personal pronoun μου-εμένα etc http://ebooks.edu.gr/modules/ebook/show.php/DSGYM-A112/621/4006,17974/