Ich trinke täglich Wasser.

Because trinken must agree with the subject and the tense. Here the subject is ich (I) and the tense is present. The correct 1st‑person‑singular form is ich trinke.

• trinkt is 3rd‑person‑singular (he/she/it drinks).
• trank is the simple past form (I drank).

täglich is an adverb of time. In a German main clause with subject + verb in position 1–2, the usual order for adverbials is Time → Manner → Place. Objects (direct or indirect) typically follow these adverbials. So you get:

1. Ich (subject)
2. trinke (verb)
3. täglich (time)
4. Wasser (object)

Yes. You can front the time adverb for emphasis. That triggers inversion (verb stays second):

• Täglich trinke ich Wasser.
  This is equally correct and simply shifts the focus to “every day.”

Wasser is in the accusative case because it’s the direct object of trinken. In this sentence there’s no article or adjective to show case endings, but if there were, you’d see the accusative ending. For example, with an article:

• Ich trinke das Wasser (nom. das Wasser → acc. das Wasser).

You have two main options, depending on what you want to negate:

1. Negate the time adverb:
   Ich trinke nicht täglich Wasser.
   (“It’s not daily that I drink water,” focus on frequency.)
2. Negate the object itself:
   Ich trinke täglich kein Wasser.
   (“I don’t drink any water daily,” focus on denying water.)

Invert the subject and verb, keeping the adverb in place:

• Trinkst du täglich Wasser? (informal)
• Trinken Sie täglich Wasser? (formal)

Yes. jeden Tag literally means “every day” and functions as a time adverbial, just like täglich. Both are interchangeable in this context:

• Ich trinke täglich Wasser.
• Ich trinke jeden Tag Wasser.
  täglich is slightly more formal/concise, jeden Tag a bit more conversational.