He's an American because he got naturalized citizenship. According to the State Department and the Supreme Court, at a minimum, he qualifies as an American.
Not if he immigrated here illegally (which he did, according to his brother). There’s no valid path to naturalization via an invalid/fraudulent lawful permanent resident status.
He is currently a naturalized American citizen. For him to lose that status, he would have to be stripped of it by a legal process, commonly called denaturalization. [0] It is not enough for people to accuse you of having committed fraud in naturalization.
> There’s no valid path to naturalization
I think it is correct to say that your naturalized status can be unwound if a prosecution against you is successful, but until that happens, you are considered an American citizen. Presumption of innocence and all that American stuff.