Die ersten Beiden, ja. Der Vater sieht das erste Kind. Die Brüder essen das erste Menü. Die ersten drei haben Bücher.
Why is ersten used with Beiden? I presume it's nominative. Even if it was accusative I would think it would be feminine (erste).
Second sentence. Why is it das erste Kind. In this case it's accusative and a neuter noun so I would presume just erst. Same with the third sentence.
Why is it die ersten drei? -en I associate with accusative masculine but numbers are feminine.
Ordinal numbers (erster, zweiter, dritter,... - first, second, third,...) can be used like attributive adjectives and for this reason they are also declined like adjectives. Adjective endings are not identical with the endings you already know from the articles (e.g. der, dem, den, etc.).
Die bestEN beiden, ja.
Der Vater sieht das schönE Kind.
Die Brüder essen das gutE Menü.
Die letztEN drei haben Bücher.
As you can see, the endings of adjectives and ordinal numbers are identical here.
For more information on adjective endings, see: http://coerll.utexas.edu/gg/gr/index.html?si=adj
PS: In the sentence "Die ersten beiden, ja", we are dealing with accusative or nominative PLURAL ("beide" is more than one), not with a feminine singular form. The last sentence too uses a nominative plural form ("three" is short for "three people/contestants/boys, etc.", ie. more than one), not a feminine singular form. You are right that numbers are feminine, e.g. "Die Drei ist eine schöne Zahl" ("'Three' is a beautiful number"), but here we're not talking about the number itself but using it as a shorthand form for "three people/boys/men", etc., i.e. to refer to a plural noun.