He doesn't have 'a' hair.

“He doesn’t have a hair.” (uncountable)
“He doesn’t have hair.”?

It’s the 2nd one right? Because we should never use ‘a’ before any uncountable… ?

Both are possible, but the second (the uncountable version) is the more likely. The first one, which is the countable version, might be used for emphasis. In both cases, he is bald.