For your first question I would probably go with "on" and add a "The" behind the blacklist, if it has a specific connection to something, because the word "blacklist" has, in the most cases, a specific connection to an event/action or something else and then, if you want to allude to it, you should use "The". But if it has no connection to an event or something or you just don't allude to that "Blacklist" , you can go without the "The" (If I am wrong, I would appreciate if you would correct me, thanks :D) And for your second problem, you can usually go with both. Maybe one option is more suited for that type of context or the other option for another type of context, as long you use one of them, you should be good to go.