Yes he was tested for mites/mange- they said about 7/8 months ago that it was garden mites and they had all left his body but they said they couldn’t be 100% sure that’s what it was
Personally, I would not give Nexgard to a dog with a compromised immune system. Especially, if it's winter (I also would avoid any vaccine boosters until he was healthy again).
Probiotics? Definitely. Anything that would build up his immune system.