Is it possible to remove tokens from dead projects/tokens that are totally useless and worth $0 from my wallet? Do I just send them to a random address? I don't want to burden anyone else with those shitcoins 
Sure, you can send them to whatever address you want, but why? You'll use gas for no good reason... I have about 10 dead tokens, i really don't care. I just ignore them.
Very wise reply, why send the dead tokens out when you will still waste gas fee. What i normally do is hide them if the wallet permits or just ignore as mentioned. What harm does it do to your wallet? So what's the essence worrying about dead tokens in your wallet. Also a token i tagged dead in my wallet surprised me, the project rebranded and i swapped the tokens and made close to 100$ from it.