If they like quartet music, I would say go ahead and include plenty of that. I think if you change the key the songs could work fine for a female choir. Working with them first on their kind of music can help them to see you as an ally.
As far as teaching parts, the main thing is repetition (although it sounds like with the choir you're working with, it may be a challenge to get them to commit to the repetition it takes to learn parts well). I wrote a web article once that you might want to check out:
How to teach a choir song.
If you have trouble figuring out what the parts are in order to be ready to teach them, once again repetition and practice will sharpen your skills. And there are also websites where you can get practice tracks with the individual parts for particular songs (the link to mine is in my sig line --
ChoirParts.com).
For trying to introduce newer music, I would suggest that you bring it in gradually and maybe start with "older" new songs. First some contemporary music from the '70s, then work your way up into the '80s, and so on. And sometimes even if a person isn't into the musical style of a particular song, they might get into it if they really like the lyrics. So try to find songs with a strong message that fits in with the major themes that their pastor emphasizes in his preaching.
God bless.