In מה נשתנה, first it says הלילה הזה which is זכר and then it says הלילות which is נקבה. Do any commentators theorize why it switches gender?
R. Eliyahu of Vilna (the Vilna Gaon) is quoted as having asked this question. A presentation of his approach (excerpted below) by R. Mordecai Kornfeld, can be found here:
In fact, notes the Gaon, the night is feminine in its very essence. It is for this reason, the Gaon explains, that many positive commandments ("Thou shalt...," as opposed to negative commandments -- "Thou shalt not...") must be performed exclusively during the daytime. (Examples of these are blowing the shofar on Rosh Hashanah, holding the four species on Sukkot, wearing Tzitzit and Tefillin, etc.) This is in accordance with the "feminine" nature of the night. Just as women are exempt from fulfilling these positive commandments (see Mishnah Kiddushin, 29a), so too, the night, in its role as "female," is "exempted" from all those Mitzvot. The exceptions to this general rule are the Mitzvot performed on the seder night: the eating of Matzah, Maror [= bitter herbs] and (in former -- and future -- times) the paschal lamb; and relating the story of the Exodus. The Torah earmarks these commandments to be performed exclusively at night. (It may be noted that the Mitzvot of the night of Pesach apply to women as well, even though positive commandments that are holiday-related generally do not apply to women -MK.)
This, asserts the Gaon, is the deeper meaning of the Haggadah's question: Why is this night (HaLaylah) "masculine" (HaZeh) in its properties, being laden with positive Mitzvot, whereas all other nights are feminine in nature?
[As an aside, and as noted by Kazi bácsi in a comment to the OP, the question of the Vilna Gaon is very difficult to understand in the first place. לילה, despite its plural form of לילות, is clearly a masculine noun, and always appears in Tanakh with masculine adjectives. R. Kornfeld in the linked article presents a possible approach to understand the intent of the Vilna Gaon.]
There are words in Tanakh that are sometimes masculine and sometimes feminine, but לילה is not one of them. לילה is masculine and לילות is masculine. The form usually indicates the gender but is not definitive. Kazi's is good advice: the adjective will indicate the noun's gender. There is no such thing as a feminine noun that takes a masculine adjective. With all respect to the Gaon, I don't think he was offering a grammatical explanation.
The general rule for feminine nouns ending in ה is that they have a kamatz gadol followed by a ה. Also, the stress is on the final kamatz-ה sequence (i.e. the ultimate syllable). The stress on לילה is on the penultimate (second-to-last) syllable (i.e. the first ל). The final kamatz-ה is probably the locative ה which expresses movement towards or into (so לילה would technically be rendered as “into the night”) as a substitute for אל or ל (as Rashi notes in many places). For example, we say ביתה, מצרימה, ירושלימה, הרה, etc.. The word for night is actually ליל (patach under 1st ל and chirik under the י). I can’t find the nekudot on my phone so I have to spell it out. We find the phrase ליל שימורים with ליל in construct form and thus having tseirei beneath the first ל as is the normal vowel change from absolute to construct for all nouns with dual endings.