Yes you need No and PO for everything in the tank. The up side of having a refugium doing it is it regulates its self. Less food less growth. And likely wont strip the water of nutrients, if you suspect it may be, you trim the chato and spot feed the coral. GFO just strips until its saturates.
zero also means its undetectable at the level of your test. If you have detritus collecting in the back and hair alge growing, you have enough Po and No in the system. Its not zero.
If you have an AIO yes the back chambers collect detritus. in my JBJ, I started doing all the WC from the back by stirring it up with a baster then siphoning it out.
The detritus in the chato is normal as its acting as a mechanical filter like floss and collecting junk. I always ran foam or floss right at the return to cut that down(like a sock). Personally I would rather have it in the chato, floss and chambers than back in the tank, because thats where it will go instead and then you dont see it and cant get it out. Its one of the things that led to my JBJ decline.
Its a crazy thought but if your getting better growth from the hair algae than chato you can fashion a mini turf scrubber instead, just by putting some "plasitc canvas" in and letting the hair grow there.
IMO you want the hair in the back or sum or fuge, thats what keeps it out of the tank.
FWIW I have seen a few threads from new sump owners who are surprised at how gross their awesome expensive sump gets not always realizing that's its job.