B (He seems to have applied it) sounds more natural / frequent to me. It means that you think he has applied it, or that it looks like he has applied it. There is no reason to think that he hasn't applied it. A sounds a little strange. I also think the meaning might be different. "He has seemed to apply it" would mean that you don't think he actually did apply it, that he only appeared to or pretended to. That's the opposite of B. Anyway, B sounds more natural and A sounds odd. I don't know which one is a better match for the meaning you want to express.

This is correct: It seems that he has applied it. He seems to have applied it. A is not correct. B is correct.

"He seems to have applied it." is correct but needs more information. For example "He seems to have applied the paint properly." or "He seems to have applied the glue to the wood."