If it is at all like what I had done, the mapping is a simple ultrasound of the veins and arteries in the arm where they will create the fistula. No pain no problem. They use a gel and a smooth ultrasound wand. Tell him no need to be nervous about the mapping. It helps the vascular surgeon to plan his/her work before going in.
I don't know why they're waiting so long but if your brother is feeling like crap (and it sounds as if he is) then he should really push that with his nephrologist and say that he doesn't want to wait any more. He may need to be persistent. Everyone is so different and some feel OK with terrible numbers and others (me included this time around) feel dreadful with not so bad numbers.
If I were your brother, I'd mention what happened to your Dad and say how petrified I am of that happening to me and that I don't think I can hold off any longer. It may be a resource issue depending on where you live but I'd push and push.
Good luck with all this and come here often.