Question about KOS-MOS and NG+

Hey guys, I just finished XC2 and can finally visit this sub without worrying about spoilers lol. I currently have Zeke as KOS-MOS' driver, but I always use her with Rex by using his master driver ability. I imagine that when you start NG+, I won't be able to use her until chapter 8 is that right? Also, if I use an overdrive protocol before starting the NG+ then I should be able to use her from the start?

One more thing, do you guys recommend getting all rare blades (I'm missing 10) and completing all sidequests before starting NG+ or is it a waste of time? Any tips before starting NG+?