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 
To avoid you regretting later why not just click on hidden button to hide the tokens from sight? You never can tell if those tokens you call worthless now will later rise once activities and publicity on them begins. There is no harm in keeping many tokens in your wallet. Scrolling down to find tokens or using the search engine on your wallet should not be any problem for anyone. I suggest you leave them in your wallet but hide them.
I can understand maybe how Op is having expectation of bull from those shit tokens in that wallet. And your suggestion of using the hide button is good because of the future, to avoid total regret because if deleted, it is gone when you forget the decimal, erc20 name etc, that is worst.
But talking about deleting, if the token was in exchange and got delisted or on some aspect where the token was deleted already from an exchange maybe because the shit token is worthless, the team abandon the project for long and no longer active in all social media, I think you can delete because the project has been scammed or exit.