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.
I have been really thinking about disposing shitty tokens off my wallet for so long, but there is nothing like delete in myether wallet, I would prefer to waste gas and send them to any random wallet than sending them to a wallet I still hold the private key in the name of separation, do you know why? I have a bounty that I got over 200k of its token but its not worth $1 I can't keep such shit in another random wallet.