Huh? Being American doesn't entitle you to prosperity. If your "personal legal librarian" (not even sure what that is, are you talking about a paralegal maybe?) says you specifically have a case for slander, then your "personal legal librarian" doesn't know the law very well. Slander has to do with oral presentations of defamation. Libel is when defamation law refers to a written defamatory post/comment.
Also, I can just about guarantee you that almost nobody on the BF platform cares about how well you play csgo. You got banned due to evidence of a cheat. Your screenshot having a tab open for "undetectable csgo cheats" doesn't help your case in any way. And besides, banzore can ban you on whim. It's a private server, hosted by a private entity, with no written contract with the people playing on their server. They can "legally" ban you just because they feel like it.
Also, I can just about guarantee you that almost nobody on the BF platform cares about how well you play csgo. You got banned due to evidence of a cheat. Your screenshot having a tab open for "undetectable csgo cheats" doesn't help your case in any way. And besides, banzore can ban you on whim. It's a private server, hosted by a private entity, with no written contract with the people playing on their server. They can "legally" ban you just because they feel like it.