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

Yes, I think it is possible but you don't need to send it to a random address. You are just wasting some of your money for transaction fees. There will be nothing wrong if you will keep it for a while, it is not a burden right? Just keep it in your wallet maybe someday it may have a high value just like any other coins though these shit coins can really be annoying if it will not have any value in the future.