He told me he wanted me to die because I asked 'would you like some dinner?' so I told him it's time for a time out.
I'm very confused by this OP, he said he wants to die and you thought the appropriate response was to punish him by shutting him in his room? I'm sorry to be harsh but don't you think that might be why he thinks you hate him?
He's telling you that he absolutely can't cope with the big emotions inside him and he needs to see you be calm and have control over this situation so he can feel safe. When he says he hates you and gets really angry you need to allow him to get that anger out and over with safely and with love. You need to be clear what is and is not ok - ie provide him with something he can hit like a beanbag, but that hitting you or breaking things is not ok. Tell him you love him no matter what and mean it, stay calm and be clear, make him feel like you have control. Crying in front of him over his behaviour is really not going to help him IMO.
Look for things that may be triggering these outbursts - write everything down and see if you can spot any patterns. Have you ever given in to him having a tantrum and given him what the wants? That is something you need to avoid at all costs. If he can't cope with shopping because he always wants something and can't cope with no - then don't take him. Order online instead. Don't put him in situations you know he can't handle right now. Don't ask too much of him. Don't ask him if he's ready for dinner just tell him dinner is ready.
Just be clear, calm and consistent at all times with lots of talking about what is going to happen today (to prepare him for things) warn him before changes in activities and have as much of a routine that is the same every day as you can - that might all really help him. I'd say he also really, really needs his own safe space, a bedroom to himself if he doesn't already - but don't make it a place for punishment, it needs to be a good, safe space.
I think he's feeling really unsafe at the moment - quite possible due to school - and you need to make home as safe a place as you can while you try to work out what's going on.