That's an awful lot of questions about a character who is hardly even in the story. What is Auntie Reed's style of speaking? Well, I could say that she uses evangelical jargon by calling Langston a "Lamb of God." However, she only says a few words. She tells the preacher Langston's name, and then she says to Langston:

“Langston, why don’t you come? Why don’t you come and be saved? Oh, Lamb of God! Why don’t you come?”

By the way, these words are a paraphrase of the hymn "Just as I Am," which is often sung during altar calls in evangelical and fundamentalist church services.

How does her appearance explain aspects of her character? Your guess is as good as mine. Hughes doesn't describe what she looks like.

Does the reader know what she's thinking? Not for certain. We can guess that she's worried because he's the last person to go forward for salvation.

How do other characters perceive her? There's no way to tell. Does the preacher call on her because she is known to be a spiritual woman or is it just because she is Langston's aunt?

What do her actions tell us about her personality? This is one question we can answer with certainty. She invites Langston to church, prays over him to be saved, counsels him to go forward, and embraces him and rejoices when he says he is saved. Her actions tell us that she is a faithful Christian. Hughes doesn't give any hint or indication that her faith might be false.