Yes, we always put the nouns after these words(сколько, много, мало, несколько, большинство и меньшинство) in the genitive plural. When the nouns are countable, they stand in the Genitive Plural (сколько вопросов), when uncountable, in Genitive Singular (сколько воды) — like in English, I guess (how many questions/how much water).

(By the way) It sounds better in russian language: В реке много рыбы

"много" always implies the question "чего?/кого?" много (кого?) людей, котят, птиц много (чего?) камней, машин, еды These are questions of Genetive case. You cannot use Infinitive case with this word.

Still are you not able to understand that genitive case expresses a belonging of ruled word to a ruling one? Много рыб (A lot of fish) Берег реки (A bank of river) Монитор компьютера (A display of computer)

This is it! Really in these examples a word 'some' is omitted but it is implied. If you don't want to imply use accusative case (in the examples where ruling word is a verb). Он не читает газеты. Ты хочешь молоко?