Question 1:
A. I saw him being angry.
B. I saw him angry.

What are differences in A and B? In meanings? Or just forms are different?

Question 2:
C. I saw him being silly.
D. I saw him silly.

I understand C. But I don't think D means anything thus invalid. Then why is the sentence B in Question 1 considered valid?

Thanks in advance.

B is a bit weird - I saw him looking angry, maybe.

Even A: I saw him acting in an angry manner, I saw him acting angrily.

Maybe because "anger" is an emotion, not a behavior, while "silly" is a way to behave. It's easy to see someone being silly, but you can't necessarily tell that someone is angry.
Thanks, GG.
Being silly can be seen but anger cannot be seen at times. You are right.