I think this is the reason many courses do start with the masu form. I actually started by learning the dictionary form, with some examples with the masu form in text snippets / exercises and it made it a lot easier for me to learn, especially when you come to the point where you learn to distinguish ichidan and godan verbs
飲む・のむ・nomu・"drink" the dictionary form of the verb used in casual speech
水を飲む mizu o nomu - I drink water (casual)
飲みます・のみます・nomimasu・"drink" the conjugated polite (-masu) form used in polite speech.
水を飲みます mizu o nomimasu - I drink water (polite)
"Nomi" is the verb stem that polite conjugations are attached to.
水を飲みません mizu o nomimasen - I do not drink water (negative polite)
水を飲みました mizu o nomimashita - I drank water (past polite)
水を飲みませんでした mizu o nomimasendeshita - I did not drink water (past negative polite)
のみ is just a verb stem
飲む「のむ」(dictionary/casual)・飲みます「のみます」(polite) is the verb "drink"
飲み物・のみもの is the noun "a drink"
As answered directly above this as well, のみ is only the stem used to conjugate the verb to the polite -masu forms; it is neither the full verb or the noun
飲む・のむ is the verb "drink"
お酒・おさけ more accurately refers to alcohol but it is accepted in the sense that "drink" is a colloquial term for alcohol in English. "to go drinking" in English always means to drink alcohol, even though the verb "drink" itself doesn't actually have that specific meaning.
nomi is only the verb stem used to conjugate the verb.
Nomu is the dictionary form/informal present tense which Duo mostly wants you to know. This is the base form needed to know how to conjugate the verb later.
Nomimasu is the polite present tense conjugation and should still be accepted, though this is an intro to Hiragana lesson so it's probably wanting you to keep it simple.
The noun is nomimono (lit. Drink-thing)