Wortbildung does rule ;-), although it's complicated.
The verb rule that you propose seems correct to me.
For nouns, there are just too many different ways and reasons of combining nouns. The most common ways are to either use the plural:
Kinderschuh, Kinderschuhe (it's not Schühe but Schuhe, although it's Kühe)
or the genitive singular, where that makes sense (relation of belonging):
Very often, when the first noun is a specifying property of the second, they are just concatenated in nominative singular form. You can probably discuss at length about why it's used this way in each of these words, but it sometimes seems quite arbitrary really.
Meerenge (Why not Meeresenge?)
Muttertag (Why not Müttertag?)
Gasthaus (a very old word. There's also the newer creation Gästehaus, with a different meaning)
There are also cases where the first part looks like a plural or other form, but it's actually not a plural but just using a "Fugenlaut" (see: Hals-Nasen-Ohren-Arzt (HNO-Arzt) vs. Hals-Nase-Ohren-Arzt oder Hälse-Nasen-Ohren Arzt)