Learn Hardcore German: Ich trinke Tee aus der Tasse.

Nominative/accusative feminine: die Tasse
Dative feminine: der Tasse
Using die (accusative) or dem (dative masculine/neuter) would be incorrect here.

Why is there no article before Tee?

In German, mass or uncountable nouns often appear without an article when you mean them in general or “some” of them. Ich trinke Tee = “I drink tea/I’m drinking tea.”
If you mean specific tea, you’d use a definite article: Ich trinke den Tee.
If you mean “a portion/a cup of tea,” you can say: Ich trinke einen Tee (common in cafés, like ordering “a tea”).

Can I say Ich trinke den Tee aus der Tasse? What changes?

Yes. den Tee makes the object definite and specific (“the tea” you have in mind).

Ich trinke Tee aus der Tasse = I’m drinking (some) tea from the cup (generic tea).
Ich trinke den Tee aus der Tasse = I’m drinking the tea from the cup (a particular tea already known in context).

Can I use von instead of aus (e.g., von der Tasse)?

No, not for drinking from a container’s inside. aus means “out of/from the inside of.”
von typically means “from (a person/source)” or “off (a surface).”

Correct: aus der Tasse trinken, aus der Flasche trinken
With von you’d talk about surfaces: vom Rand der Tasse (from the rim of the cup).

Why not mit der Tasse?

mit expresses “with/by means of” (an instrument/companion), not the source interior.
Ich trinke mit der Tasse literally means “I drink using the cup,” which is unusual and not how Germans express drinking from a container. Use aus der Tasse for “from/out of the cup.”

How flexible is the word order? Could I say Ich trinke aus der Tasse Tee?

Yes, German allows some flexibility. Neutral/default is your version: Ich trinke Tee aus der Tasse.

Ich trinke aus der Tasse Tee is possible, often to emphasize the container.
You can also front the prepositional phrase: Aus der Tasse trinke ich Tee (focus on the cup).
All are grammatical; choose based on emphasis and flow.

What’s the difference between aus der Tasse and aus einer Tasse?

aus der Tasse = from a specific, known cup (“the cup” in this situation).
aus einer Tasse = from some (unspecified) cup.
Both use dative; der is definite, einer is indefinite.

How is trinken conjugated here?

Present tense:

ich trinke
du trinkst
er/sie/es trinkt
wir trinken
ihr trinkt
sie/Sie trinken
In this sentence, ich trinke is 1st person singular present.

Does Ich trinke mean “I drink” or “I am drinking”?

Both. German present covers simple and progressive. Context decides. To stress “right now,” add gerade: Ich trinke gerade Tee aus der Tasse.

How would I say it in the past?

Conversational (Perfekt): Ich habe Tee aus der Tasse getrunken.
Narrative (Präteritum): Ich trank Tee aus der Tasse.
Both are correct; Perfekt is more common in speech.

How do adjective endings work here (e.g., “from the red cup”)?

With definite article (dative fem.): aus der roten Tasse
With indefinite article (dative fem.): aus einer roten Tasse
With no article (dative fem., strong ending): aus roter Tasse
All mean “from the red cup/a red cup/red cup,” respectively.

What’s the gender and plural of Tasse?

Tasse is feminine: die Tasse.
Plural: die Tassen.
Dative plural adds -n to most nouns if not already there: aus den Tassen.

Can I replace aus der Tasse with a pronoun?

Yes: daraus = “out of it/from it.”
Example: Die Tasse steht da. Ich trinke daraus.
You can also keep the object: Ich trinke Tee daraus.

Can I drop Ich and just say Trinke Tee aus der Tasse?

Not in a normal declarative sentence. German isn’t a “pro-drop” language. You need the subject pronoun.
You can drop it in the imperative: Trink Tee aus der Tasse! (addressing “du”).