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.