"그는 자면서 말합니다."
Translation:He speaks while sleeping.
그는 is always he, 그 can be he, (to) him, or his according to the context. He can be 그가, but I think 그가 is also used for him like 그를. Still, be consistent. 그는 goes with 그녀는 . . .
These words are determiners (well, except perhaps his/hers?, but they might as well be in a reflexive way). The sense of the particle is included as I see it.
그 and 그녀 are pronouns, not determiners and
as you can see, they take particles like normal nouns.
if you want, you can attach particle 의 to them to
form determiners with the meaning:
Yeah, exactly -- I was tired and don't know how to describe what I was thinking. Sorry about that. They have roles in the sentence like particles.
I've seen them (그, 그녀, 그들) called pronomials without the particles, "related to pronouns". It looks like you should add 의 것 to get the reflexive forms: 그의 것 (final) his, 그녀의 것 hers, 그들의 것 theirs -- though I'm not sure whether it's entirely necessary (it isn't at all in Japanese) as Google translate, say, is inconsistent there.