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 
That would be one of the easiest way to get rid of them since some of those shitcoins cannot be sold and looking for an exchange to sell them would take too much time. You can just ignore those Shitcoins since it would also be fine to leave those coins there so that you can keep track of Old Tokens that might have a same name with incoming new projects.