The Yad Peshuta of Rav Nachum Rabinovitch, shlita, ad loc., sources the Rambam's ruling from the Sifrei (Shoftim 157 Finkelstein pp. 208-209):
איש נכרי מכאן אמרו, האיש ממנים פרנס על הציבור ואין ממנים האשה פרנסת על הציבור
"a man who is a stranger" - from here they said, a man may be appointed as an official over the congregation, but a woman may not be appointed as an official over the congregation
The Yad Peshuta suggests a possible distinction between this law and the earlier related passage of the Sifrei - מלך ולא מלכה - "a king" but not a queen - that perhaps only with regard to an actual queen would the prohibition even include where the congregation willingly accepts her authority, whereas this law might only restrict involuntary subjugation.
Thus with regard to 1., it might depend on how the position of CEO is determined.
Additionally, it seems reasonable to draw a distinction, based on the language of the Sifrei above (פרנסת על הציבור), between communal/government positions, and private companies, since, after all, women are certainly allowed to hire Jewish workers/employees.
In addition to the above arguemnts, with regard to 2, the Babylonian Talmud (Yevamoth 102a) indicates that a proselyte is allowed to judge his fellow proselyte:
גר דן את חבירו דבר תורה שנאמר (דברים יז, טו) שום תשים עליך מלך אשר יבחר ה' אלהיך בו מקרב אחיך תשים עליך מלך עליך הוא דבעינן מקרב אחיך אבל גר דן את חבירו גר
By Torah law a convert may judge his fellow convert, as it is stated: “You shall set a king over you, whom the Lord your God shall choose; one from among your brothers you shall set king over you” (Deuteronomy 17:15). [The Gemara deduces from the terminology of the phrase] “over you,” [i.e., when presiding over Jews by birth either as a king, a judge, or any other official, that] from here it is where we require that the official must be: “From among your brothers,” meaning a Jew by birth. However, a convert may judge his fellow convert, [as the requirement of “one from among your brothers” doesn’t apply when presiding over fellow converts].
Assuming the Talmud's inference is based on an equation between the "you" of אחיך and עליך, the logic would seem to apply to women having authority over other women, as well.