I agree that it's most likely his way of dealing with the big change in his life at the moment, especially as the teachers say he's well behaved at school - it sounds like any frustration he's getting there is building up and building up and it's just coming out at home over the tiniest thing. This is actually a positive thing in a way (bear with me!) as it means that he feels safe enough in your presence to let his true feelings come out, and knows that you will still love him.
I think that you need to really really try to remember these are his feelings coming out which are probably big and scary for him, and try not to take it personally, even if he is saying things like he wants you to die, or go away, or be crushed(!) - all that he's expressing (clumsily) is "You are really annoying me at the moment and I need you to get out of my face" (Not saying that you should necessarily leave him alone at these times BTW.)
If he's hitting you when you are trying to speak to him, then don't even try speaking with him when he is that worked up. I agree that this is NOT a situation you can ignore, but I don't think that punishments or rewards are the way forwards either - it's more about teaching him to manage these feelings. You do need an immediate strategy to stop/prevent any damage being done to people or things. Either take him to another room so he can calm down, or if he's being too destructive there, won't stay, the idea doesn't appeal (or whatever) restrain him from behind in sort of a hug which means he can't move his arms, kick, or bite. (If you hold his arms down by folding yours around his whole body, pinning them to his sides, then it won't hurt him unless he is really fighting against it. Don't grip his arms in your hands because you could end up hurting him.) Tell him in a calm voice "I know that you are really angry, DS, but I cannot let you hit/kick/me/your brother/break things." Hold him until he feels calm - he probably will scream, cry, struggle and insist that you are hurting him, and it will feel like you've been holding him for ages, but he will calm down shortly. Keep reiterating "It's only hurting because you are pushing away from me. I'm going to hold you like this until you calm down, because I can't let you hurt people. We can talk when you are calm. It's okay to feel angry, but we need to find you a different way of showing it." (etc etc depending on whether talking is calming him or winding him up more, or even whether it helps you keep calmer.) If he starts saying horrible things like "I hate you!" either ignore them, or just say "Okay". You can talk to him later about how those kinds of things are hurtful to say, but right now if you point that out he'll probably say "Good!" Once he is calm, you can ask if he wants a cuddle, and if he feels better now, and then something like "Daddy was hurt when you kicked him. How do you think we could make him feel better?" (And then prompt with a cuddle, kiss better, apology, etc, if he doesn't suggest anything helpful) and remind him that we don't kick people and if he is really cross he can kick the sofa or go outside and kick his ball or something, let him do the "making better" thing and let it be over.
When you or your partner shout (we all do!) how do you manage this? Do you apologise for it, or do you just accept that you shouting = an unpleasant consequence of DCs winding you up? I've had massive success with reducing DS shouting at me by trying to catch myself when I am shouting and apologising for it, and if he asks me to stop shouting or talk nicely then I do, even if it takes a big effort. Also asking him to "talk nicely" rather than "Stop shouting!" (illustrated fantastically yesterday - DS was shouting, DP said "Don't shout" in firm, slightly raised but not quite shouty voice, DS ignored him, I said "Talk nicely please, DS" and he immediately changed his tone of voice 
)
I also find with DS that it's worth having a neutral, non-telling-off conversation about how he feels when he gets angry, much later, like before his story at bedtime. I know they say that you have to deal with things there and then, but when they are massively worked up is not the time to try, because 1) they won't listen, 2) they will be too angry to see any other point of view than "I am right and you are NOT FAIR!"
With the alternative release thing I think you really have to keep reiterating it, it doesn't work to just suggest it a few times or give up because he doesn't find it satiates his anger the first few times. Always remind him too if you think he's about to strike. Physically move him to the thing he is allowed to hit/kick/bite if he doesn't look like he's going to do it of his own accord and if he's still resistant then do the restraining thing. You can also do something which seems unrelated but which might be appropriate at school, such as giving him a piece of paper and a crayon and saying "Show me how angry you are! Draw me a picture to show how cross you feel!"
Hopefully, this is just a phase, related to starting school, but even if it is this stops the immediate effects and shows him that you are not going to let him behave in that way. I don't think you need to add toy-removing or other punishments on, I think that's just likely to escalate things. Also DS is going through a similar phase of objecting hugely to what seems like ridiculously small things, and it helps to give him options at every opportunity, such as "Do you want to climb into your carseat, or me to lift you up?" "Would you like the pink cup, or the green cup?" and being a bit flexible ie if he runs in shouting "No I wanted to get it out of the cupboard!!" don't react immediately with consequences to that shouting/whining, but say "Okay, WAIT! You can get the cup, I'll put it back, but you just have to ask me nicely." and then when he asks nicely and gets to get the cup himself, say "See? If you ask me nicely, it's fine. Try to remember to ask nicely first next time."
It's exhausting, this, isn't it?
