Learn Hardcore German: Ich kenne den Text schon auswendig.

Using Ich weiß den Text is generally felt to be wrong or at least very odd. For knowing something by heart, German normally says etwas auswendig kennen or etwas auswendig können, not wissen.

Why is it den Text and not der Text?

den Text is in the accusative case, because it is the direct object of the verb kennen.

The noun Text is masculine.
Masculine definite article forms:
- Nominative: der Text (subject)
- Accusative: den Text (direct object)

Example:

Der Text ist lang. → Der Text is the subject (nominative).
Ich kenne den Text. → den Text is the object (accusative).

So in Ich kenne den Text schon auswendig, den is required because Text is the thing being known.

What exactly does schon add, and can I leave it out?

Here schon means already.

Ich kenne den Text auswendig.
You know the text by heart. (neutral statement)
Ich kenne den Text schon auswendig.
You already know it by heart (earlier than someone might expect, or earlier than some other point in time).

You can leave schon out; the sentence remains correct, but you lose the idea of already. The core meaning know by heart comes from kennen … auswendig; schon just adds a time nuance.

Why is auswendig at the end, and what is it grammatically?

auswendig is an adverb meaning by heart / from memory.

In a normal main clause, German puts:

Subject in first position (Ich)
Finite verb in second position (kenne)
Other elements (objects, adverbs, etc.) in the rest of the clause, often with adverbs of manner like auswendig toward the end.

So:

Ich (subject)
kenne (verb, 2nd position)
den Text (object)
schon auswendig (adverbial phrase at the end)

Also, auswendig kennen is a very common fixed combination, so keeping auswendig close to kenne at the end feels natural.

What is the difference between auswendig kennen, auswendig können, and auswendig lernen?

These are related but not identical:

etwas auswendig kennen
You know something by heart (state of knowledge).
- Ich kenne den Text auswendig. = I know the text by heart.
etwas auswendig können
Very common in everyday German, especially with poems, songs, texts. Same meaning in practice: you can recite it from memory.
- Ich kann den Text auswendig. = I can recite the text by heart.
etwas auswendig lernen
The learning process: to memorize something.
- Ich lerne den Text auswendig. = I am memorizing the text.

So your sentence describes the result (you already know it), not the learning process.

Is Ich weiß den Text auswendig correct German?

It is understandable and you will see or hear it occasionally, but it is not the most natural choice.

For a native speaker, the idiomatic options are:

Ich kenne den Text auswendig.
Ich kann den Text auswendig.

Using wissen with a bare noun like den Text is generally avoided. wissen is normally followed by:

a clause: Ich weiß, dass … / wann … / wie …
or a question word: Ich weiß, wer das ist.

So for good, natural German, prefer kennen or können here.

Why is the present tense (Ich kenne …) used instead of something like a perfect tense?

German uses the simple present much more than English for ongoing states:

Ich kenne den Text schon auswendig.
Literally: I know the text already by heart.
Context often corresponds to English I have already learned / memorized the text.

The perfect Ich habe den Text schon auswendig gekannt is unusual and would normally be used only with a clear past-time reference, for example:

Früher habe ich den Text auswendig gekannt, aber jetzt nicht mehr.
In the past I knew the text by heart, but not anymore.

So for a state that is true now, German present tense is best.

Could I drop the article and say Ich kenne Text schon auswendig?

No, that is not correct in standard German.

In the singular, countable nouns almost always need an article or another determiner. You must say, for example:

Ich kenne den Text schon auswendig. (the specific text)
Ich kenne einen Text auswendig. (some/one text)

Without den or einen, Text here sounds wrong to native ears.

How do I know that Text is masculine? Is it always der Text?

Yes, Text is always masculine:

Nominative: der Text
Accusative: den Text
Dative: dem Text
Genitive: des Textes

Unfortunately, in this case there is no reliable rule that tells you the gender from the ending. You simply have to learn the word together with its article (for example: der Text) so that you know which forms (like den Text) to use.

Are schon and schön related? They look so similar.

They look similar but they are different words with different meanings and pronunciations:

schon = already
- Pronunciation: [ʃoːn] (like English show plus n)
schön = beautiful, nice
- Pronunciation: [ʃøːn] (the ö is like the vowel in French peu)

In your sentence it is schon (already), not schön.

Can I move schon to another position, like Ich kenne schon den Text auswendig or Schon kenne ich den Text auswendig?

Yes, but the emphasis changes slightly.

Ich kenne den Text schon auswendig.
Neutral, the most typical version. Focus is just on already.
Ich kenne schon den Text auswendig.
Now schon leans toward den Text:
something like I already know the text by heart (maybe in contrast to something longer or more difficult that you do not yet know).
Schon kenne ich den Text auswendig.
This is possible but sounds stylistically marked, a bit dramatic or literary. It strongly emphasizes schon: Already I know the text by heart.

For everyday speech, Ich kenne den Text schon auswendig is the best choice.