Is it possible to remove tokens from dead projects/tokens that are totally useless and worth $0 from my wallet? Do I just send them to a random address? I don't want to burden anyone else with those shitcoins 
Sure, you can send them to whatever address you want, but why? You'll use gas for no good reason... I have about 10 dead tokens, i really don't care. I just ignore them.
Yes, this is correct. Why should i lost my ETH to send tokens to another wallets? Actually i think there is no system that we can disable them from wallet unless transfer. So don't do this and don't lose your transfer fee just avoid them. I have also lots of tokens that has no value in $.