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 
It's your call if you want to get rid of the tokens but you should now that dead cats can bounce back to life, if I were you I'd leave them in my wallet, they can't disturb you from making transactions or can they? Shitcoins can do some magic, keep holding them