ve'eshet Noach ushloshet neshei vanav (Gen. 7:13) ('and Noach's wife and the three wives of his sons') Rabbi Chanoch Gevhard pointed out that the word shloshet is irregular and that the suffix Tav, like Heh is, in numbers, a characteristic of masculine. For example arba imahot, sheloshah avot (Echad mi yodea? Haggadah shel Pesach). Similarly, when in construct state (although this is not a standard type of construct state) we have tesha mei'ot (Gen. 5:5) (mei'ah 'a hundred' is feminine) but letish'at hamatot (Num. 34:13) (mateh 'a tribe' is masculine) we can see here that the suffix Tav in tish'at indicates masculine, while neshei is feminine, so we would have expected shelosh. How do we explain this?

The rules of masculine and feminine numbers are explained in Mislol (This is a classic work of Hebrew grammar of the late 18th century. The title page states that it is "by the great grammarian Chaim ben Naftali Hirtz Kesslin of Berlin, a descendant of the truly famous eminent scholar, the author of the Tosefot Yom Tov , Vilna 1858). There we find:

You can clearly see that the gender of numbers is indicated in reverse to other nouns that have Heh at their end to indicate being feminine, and masculine does not have a Heh. In the case of numbers up till ten, the masculine has Heh at the end, and in feminine there is no Heh. And so in shemonah ('eight') where the Nun has a Kamatz, it is masculine, and when the Nun has a Segol it is feminine. However, from ten and above, it is without Heh for masculine (achad asar, sheneim asar, sheloshah asar,etc. until tish'ah asar), while feminine is with Heh (achat esreih, sheteim esreih, shelosh esreih, etc. until tesha esreih). (p. 261)

In the Mislol I did not find information on the suffix Tav, but in R' Moshe Chaim Luzzatto's (Ramchal) Book on Grammar (Sha'ar 2, Part 1, Ch. 3, The Number Noun; ed.ition of A. S. Brieger, p. 20) there are tables of the various forms of numbers. The numbers with the suffix Tav are listed as construct masculine, so it is clear that in the opinion of Ramchal, the Tav is a suffix for masculine construct numbers. Despite the contention of Devek Tov (quoted by Rabbi Chaim Dov Chavel in his anthology of commentaries on Rashi, Exod. 10:23, Mossad HaRav Kook), a check in the Concordance will demonstrate that in most occurrences, the suffix Tav is masculine. However, there are exceptions: sheloshet hanafet (Josh. 17:11); lishloshet achyoteihem (Job 1:4); arbat (ketiv) kanfot (Ezek. 1:10; 1:16; 1:18). Ramchal's tables are based on the majority of cases in Tanach. The Gaon of Vilna maintains the same principle. He writes: we follow the majority of cases in Tanach (Shulchan Aruch, E.H. 129:28). Rabbi Avraham ibn Ezra wrote:

You should be aware that Heh at the end of a word is a sign of feminine. Only in arithmetic is this inverted for sheloshah, tish'ah, all of them are masculine, and the sign of the feminine is the dropping of the Heh - shalosh, arba, up to eser. And if they are put in construct form with a suffix Tav the masculine is mixed with the feminine. For example: lishloshet achayoteihem. (Job 1:4; Yesod ha'Dikduk which is Sefat Yeter, ed. Nechemiah Aloni, Mossad HaRav Kook, 1984, p. 168)

There is an editorial note to this passage pointing out that nowadays speakers of Hebrew take care to distinguish and add the suffix tav for masculine and omit it for feminine. This he points out is not proven from the sources in our literature. Professor Aloni is saying that the view of Ramchal has become accepted as normative. It seems to me that the views collected above are not in direct dispute. R' A. ibn Ezra is describing the language in the Tanach, the Gaon of Vilna is setting the standard for the writing of gittin, and Ramchal is prescribing how to write Hebrew. The latter two follow the majority of cases in the Tanach.

Why is one Mem without a Dagesh and the other with a Dagesh?

vayimach … vayimma:chu (Gen. 7:23) The first Mem is without a Dagesh, the second one with! (The Maharal of Prague wrote in his commentary Gur Aryeh that in his books both have a Dagesh - erroneously.)

Rashi wrote a comment on the first of these: vayimach 'its linguistic form is vayif'al' (that is to say Kal) and then he or someone else added 'and not vayipa'el' (that is Nif'al). Rashi goes on to say 'It is the same type of verb as vayiven and vayifen; every word that has Heh at the end such as banah, machah, kanah, with a prefix Vav-Yud, has a Chirik under the Yud. According to Rashi because this is Kal there is no place for a Dagesh in the Mem. On vayimma:chu R' A. ibn Ezra wrote nimcha indicating that vayimma:chu is Nif'al. In the future, Nif'al has a Dagesh to compensate for the Nun of the Nif'al that does not appear.