1. He stood silent.

Question

2. He remained quiet.
3. He lay speechless.
4. He stood silently.
5. He stood quietly.
6. He was standing arrogantly.
7. He was standing silent.

(Are they all grammatical? From #1 to #3, adjectives are used. In the other sentences, adverbs are used.)

Answer 1

Yes, they are all correct.

In the sentences with adjectives, the verb acts as a state of being verb. The adverbs follow action verbs.