Learn Hardcore Japanese: watasi ha kenkou no tame ni mainiti mizu wo nomimasu.

は marks the topic (“as for me”) and sets 私 as what you’re going to talk about. If you used が, you’d be marking 私 as the grammatical subject in a more neutral or identifying way (often used to answer “Who drinks water?”). Here, 私は…飲みます emphasizes “I” as the topic rather than just the subject.

What does 健康のために mean and why do we need both の and に?

Breakdown:

健康 = health
の = genitive/linking particle, turning 健康 into “health’s/health-related”
ため = “sake” or “purpose” (“for the sake of health”)
に = particle that marks direction or purpose when attached to ため
Altogether, 健康のために = “for the sake of health” or “for my health.”

Why is ために used here? Could we use ように instead?

ために expresses a direct, intentional purpose when the subject takes an action to achieve that goal.
ように expresses a more indirect aim, wish, or outcome (often with verbs you cannot directly control).
Since “I drink water” is a direct action to achieve “health,” ために is appropriate.

Why is there no particle after 毎日?

毎日 is an adverb meaning “every day,” so it directly modifies the verb. Time adverbs in Japanese generally do not require particles (unlike some other languages).

Why is 毎日 placed before 水を飲みます? Could it go elsewhere?

Japanese word order is flexible, but adverbs and adverbial phrases typically come before the verb. You could also say: 毎日、私は健康のために水を飲みます。
or
私は健康のために毎日水を飲みます。
All are correct; the most natural is to keep 毎日 close to the verb.

Why is there an を after 水? Can we drop it in casual speech?

を marks 水 as the direct object of 飲みます. In very casual speech, you might hear the particle dropped (水、飲む？), but in almost all written or polite spoken contexts, you keep を.

Why is the verb in polite form 飲みます instead of plain 飲む?

This sentence uses the ～ます form for politeness or formality. The plain/dictionary form 飲む is used in casual speech or writing among friends. Both mean the same, just different levels of formality.

Can we omit 私は since it’s obvious who’s speaking?

Yes. Japanese often drops the topic or subject if it’s understood from context. You could simply say:
健康のために毎日水を飲みます。
and it would still be clear.

How would you change this sentence to the past tense or make it negative?

Past tense: （私は）健康のために毎日水を飲みました。
Negative form: （私は）健康のために毎日水を飲みません。

What’s the difference between ために and ための, as in 健康のために vs 健康のための運動?

ために (with に) goes before verbs to express purpose: “do X in order to…”
ための (with の) goes before nouns to describe something “for X” (e.g., 健康のための運動 = “exercise for health”).