1. This should be present progressive : 'You're acting strange'.
You could also say 'You're acting strangely' here, without changing the meaning. However, it's acceptable to use an adjective with 'act' because the meaning is the same as 'You're being strange' or 'You seem strange' or even 'You look strange' or 'You sound strange'. This is because the adjective is describing the person at that moment rather than modifying the verb.
2. He got off the bench, very nervous.
Can you see I've added a comma here? This separates the two pieces of information - 1) He got off the bench 2) (He was/looked/seemed) very nervous. The adjective 'nervous' describes the person rather than the action, and the verb ( e.g. to be) is understood. You could also say 'He got off the beach very nervously' if you want to describe the action.
3) 'Open' is an adverb.