I always clean everything thoroughly, running it all through two dish cycles, neither with any soap. Once just for the super hot water, and then again to let it all get really rinsed in case there was any soap residue in the washer during the first go-round. It has been pointed out before, and is true, that betta, like children, need some germs in order to have a good immune system and to live healthily, but I think that having a clean tank to start out and then allowing the good bacteria to come in through daily life is a good precaution.
After the dishwashing, I put everything out on my deck for a couple of days to dry in the sun, and then you're good to go. :) Just make sure you don't use any soap or chemicals, though vinegar and water is fine. :)
Oh, and it can all be washed, tank, plants, rocks (unless you're using gravel, and then I'd just buy some fresh gravel), decorations, etc. Plants and things you are worrying about melting should go on the top rack, anything glass or hard plastic can go on the lower rack. :)
Good luck to you, and I'm sorry about your boy, but it sounds like had a good life. :)