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 
You can delete tokens from your wallet without getting rid of the tokens completely, just delete the smart contracts and add again when you need the tokens to appear again, or send the tokens from your wallet to another crypto walletJust know that shitcoins can still bring good value in future, I don't advice you to send the tokens to unknown address