Why is this "poslední", even though the feminine plural ending for adjectives is said to be "-é"? Are there more exceptions?
All adjectives with soft singular ending = -ží (boží), -ší (kratší), -čí (dračí), -ří (zubří), -dí (medvědí), -ní (polní), -cí (hrací).
A typical representative is "jarní": https://en.wiktionary.org/wiki/jarn%C3%AD#Adjective_2
There are basically two kinds of adjectives - hard (ending in masculine on -ý) which do distinguish between the genders (nový/nová/nové) - and soft (ending on -í) which do not. It's poslední muž/poslední žena/poslední dítě.
The absence of "the" is error for English, but is it so important for czech translation?
No. On the contrary, it would sound weird here. In English 'the' is part of 'last'. In Czech 'poslední' is already 'the last'
Regardless of the Czech sentence, "We are last women" is not correct English - you need the article there, so it's "We are the last women."
Similarly, you would need to include it in "We are the first women."
If there were a different adjective, for example, "Jsme mladé ženy", you don't need the article anymore - "We are young women." (In fact, it's closer to the czech sentence without the article.)
"Last" is not an adjective? I will know more English then Czech from this course!
In this case it's an ordinal number, or at least it acts as one. And as such it needs a definitive article.
It is an adjective, but it needs the "the" article when used like this. (It's not needed in phrases like "last night", "last Saturday", "We finished last.")
I put "we are the last ladies", which was marked incorrect. Is there a difference in Czech between women/ladies?