Sorry for picking this bone with you, but I thought "to be assertive for the sake of being assertive" rarely plays into your hands.
1) 就算做错了,也要摆事实,要让人觉得你错得有道理。 One word: How? Insist that you were right when you have jsut been proven wrong? Or you meant to say that you were right to be wrong? Either way, it is hard to see how one can be both right and wrong, however you spin it.
2) 这时候最简单的就是no. 如果yes, 以后你就别想管他了。 Saying "no" may be the easiest answer, but hardly the best answer. It is easy because you can say "no" by virtue of your position, but it is when you are willing to entertain "yes"s or even "maybe"s you truly start to win over lasting loyal converts. (This, of course, does not apply when saying "no" is clearly the right business answer.)
3) 哎,如果你想学汉语, 我可以教你啊。希望你的汉语比我的英语好。That is the typical loser's twisted logic. If you truly have a winning argument, your purported linguistic weakness loses not your technical forte. By the same token, if you have to resort to defensive maneuvers like using bullying tactics to beat a bully, you have already lost the moral high ground.
Now, I will content myself with being my usual humble self.