I don't do rewards and punishements. I do 'I'm the boss and you'll do as you're told'
Remove him from whatever activity it is he is doing wrong, if he throws something, take it away from him.
e.g If DS/DD were kicking the back of the chair I'd move them from the chairso they couldn't kick it, if they carried on misbehaving they could sit on the floor. I find I say 'If you can't do X properly, you can't do X at all' quite a lot.
If they had thrown books/toys down the stairs my reaction would be 'Are these for the bin then?' and just put them up somewhere. When they asked for them later I'd say 'Well, I thought you wanted them to go in the bin?' and then explain that I hadn't thrown them away because I knew they were being silly, but next time, I would.
And never argue with them, ignore strops and tantrums, tell them 'I can't talk to you whilst you're like this because I can't understand you' and walk away.
As for hitting his sister, seperate them, take one of them with you to whatever you're doing, depending on the situation, if DD is watching her fave programme for example and you're cooking dinner, make him come and sit in the kitchen whilst you cook. If she would prefer to come in the kitchen with you, turn the tv off and leave him there by himself.