Type at the singular usually lead to complement in the singular while a plural commonly lead to a plural.

This is however not an absolute rule as the Académie wrote:

Selon les contextes et le sens que l’on prête à ces groupes nominaux, on mettra l’accent tantôt sur le singulier, tantôt sur le pluriel.

The OQLF confirm the number consistency, but also gives various examples where a singular is followed by a complement in the plural. e.g.:

Cette espèce de verres est particulièrement délicate.

From the four last sentences, only quels sont tes types de femme ? looks unused.

Type au singulier entraîne le plus souvent le singulier pour le complément alors que le pluriel entraîne aussi souvent le pluriel.

Ce n’est cependant pas une règle absolue comme l’a répondu l’Académie:

Selon les contextes et le sens que l’on prête à ces groupes nominaux, on mettra l’accent tantôt sur le singulier, tantôt sur le pluriel.

l’OQLF confirme la cohérence des nombres, mais donne aussi des exemples où un singulier est suivi d’un complément au pluriel, par exemple :

Cette espèce de verres est particulièrement délicate.

Des trois propositions, seul quels sont tes types de femme ? semble inusité.

I

One can go by the BDL and learn that sometimes the s is used and sometimes it’s not while grammarians are not specially informative in what concerns this problem. One might also find relevant the following precept that can be read in the introduction to this article;

On peut néanmoins retenir quelques principes. Après les mots genre, espèce, variété, classe, forme, sorte, catégorie, type, etc., au pluriel, le complément est généralement au pluriel s’il se réfère à une réalité concrète ou que l’on peut compter, et au singulier s’il désigne une valeur abstraite non dénombrable.

However, personally, I find that this lack of definiteness is the sign of a persisting problem the solution of which does not lie in the arguments proposed.

As this ngram shows both possibilities are common.

The logic of the construction, as I personally see it, seem to indicate that in all those cases no s should be used; « genre de X », « type of X », « category of X » and others such constructions denote categories or said somewhat differently, sets, of properties, each one of those properties corresponding to, again, a set, and so, “un genre de X” is a set in which all the elements are X’s and most of the time there has to be more than one in it; therefore we are inclined to use an s ( personnes, femmes, etc.). However, in doing so we force the relation between for instance “genre” and “personne” to be one of possession: the genre is possessed by “des personnes” and not by “des militaires” or “des médecins” or whatever other category; in that sense we define the type of “genre”; if we do not use an s we are not speaking anymore about “personne” as a definite set associated to a category that those “personnes” define, but about “personne” in the generic sense, that is to say in some way as a variable over the set of all “personnes”.

• C’est un type de combattants que j’ai connus pendant la guerre.
• C’est un type de combattant, un type que j’ai connu pendant la guerre.

Saying “genre de personne” introduces a set as a subset of a known set wich is determined by the generic entity “personne”, which is a property; all the elements in this set are a “personne” and it is the set of all “personnes”; un “genre” refers to a subset of those properties and therefore to a subset; incidentally, for whom can understand the basis of the Zermelo-Fraenkel set theory, which resolved the Russell paradox, I’ll add that it seems to me that this rhymes with the axiom of comprehension in this theory (solution to the paradox), otherwise called axiom of separation, telling us that there is an existing set from which the elements can be chosen or in other words “separated”.

Albeit without authoritative support for it and on the basis of somewhat shaky personal views and déductions, that is how I perceive the logic of this construction. The outcome is that I think an s should never be used in the plain case being discussed.

There is, by the way, an analogous situation involving the preposition “à”; should we write “un homme à femmes” or “un homme à femme”?

An ngram shows that the use of s predominates whereas it is the opposite in the case considered previously (genre de personne).

II

“Type” takes an s when there is more than one; there is no difficulty here.

• Le type des personnes qui ont les jambes courtes et le type des personnes qui ont les jambes longues sont deux types de personne.