Learn Hardcore German: Mein Wörterheft liegt immer neben dem Bett, damit ich vor dem Schlafen noch etwas wiederholen kann. - My vocabulary notebook always lies next to the bed so that I can review a bit before sleeping.

You could say ist, but it sounds less natural. Native speakers usually choose liegt for flat objects on a surface, steht for upright objects (a bottle on a table), etc.

Why is it neben dem Bett and not neben das Bett?

Neben is one of the so‑called “two-way prepositions” (Wechselpräpositionen):
an, auf, hinter, in, neben, über, unter, vor, zwischen.

If there is movement towards a place (change of location), you use accusative.
- Ich stelle das Wörterheft neben das Bett.
  → I put the notebook next to the bed. (movement to a new spot)
If something is already located somewhere (no movement), you use dative.
- Mein Wörterheft liegt neben dem Bett.
  → My notebook is lying next to the bed. (location)

In this sentence, the notebook is just lying there; nothing is being moved, so dem Bett (dative) is correct.

Why is it dem Bett, but mein Wörterheft without any article?

Two different things are happening:

dem Bett
- Bett has grammatical gender neuter: das Bett.
- After neben with static location, you need dative.
- Dative singular neuter of das is dem → dem Bett.
mein Wörterheft
- Wörterheft is a neuter noun (das Wörterheft).
- When you use a possessive determiner (mein, dein, sein, ihr, unser, euer, ihr), you usually don’t add a definite article:
  - mein Wörterheft, not das mein Wörterheft.

So it’s “my notebook” (mein Wörterheft) and “next to the bed” (neben dem Bett).

What exactly does damit mean here, and why not um … zu?

Damit is a conjunction that introduces a clause of purpose:
→ so that / in order that.

In this sentence:

… damit ich vor dem Schlafen noch etwas wiederholen kann.
→ “… so that I can revise/review a bit before going to sleep.”

damit is especially used when the subject can be different in the two clauses:

Ich lege das Wörterheft neben das Bett, damit ich es schnell finde.
(I put it there so that I can find it quickly.)

You could also express purpose with um … zu, but um … zu is used only when both clauses have the same subject:

Ich lege das Wörterheft neben das Bett, um es schnell zu finden.
(Subject “ich” in both parts.)

In your sentence, the subject is in both clauses ich, so um vor dem Schlafen noch etwas zu wiederholen would be grammatically possible. However:

damit + full clause is a bit clearer and more natural in everyday speech here.
um … zu sounds a bit more formal or written, and the sentence is already fairly long.

So damit is a natural, idiomatic choice.

Why is the verb at the end in damit ich vor dem Schlafen noch etwas wiederholen kann?

Because damit introduces a subordinate clause (Nebensatz). In German subordinate clauses:

The conjugated verb goes to the very end of the clause.

So:

Main clause: Mein Wörterheft liegt immer neben dem Bett,
(verb in 2nd position: liegt)
Subordinate clause: damit ich vor dem Schlafen noch etwas wiederholen kann.
(conjugated verb kann at the very end.)

If there are two verbs (a modal + infinitive), both go to the end, with the infinitive before the finite verb:

… etwas wiederholen kann.
… etwas lesen möchte.
… etwas lernen muss.

What is going on grammatically in vor dem Schlafen? Why is Schlafen capitalized?

Vor dem Schlafen is a common structure in German:

A preposition (vor)
- a definite article in dative (dem)
- an infinitive used as a noun, a “nominalized infinitive” (Schlafen).

Nominalized infinitives are:

formed from the verb infinitive, capitalized, and
always neuter: das Schlafen, das Essen, das Lernen.

So:

vor dem Schlafen = before the act of sleeping / before sleep(ing).

This works like a noun phrase:

Ich trinke Kaffee vor dem Arbeiten.
Nach dem Essen gehe ich spazieren.

Alternative ways to say it:

bevor ich schlafe (before I sleep)
bevor ich schlafen gehe (before I go to sleep)

Those use normal subordinate clauses instead of a nominalized verb.

Does noch here mean “still”, “yet”, or “some more”?

In this context, noch has the meaning of “some more / additionally / before it’s over”.

… damit ich vor dem Schlafen noch etwas wiederholen kann.
→ so that I can (still) review a bit / review something more before going to sleep.

Nuances of noch:

still:
- Bist du noch wach? → Are you still awake?
yet:
- Hast du das noch nicht gemacht? → Haven’t you done that yet?
some more / additionally (our case):
- Ich möchte noch ein bisschen lesen. → I’d like to read a bit more.

Here it emphasizes “a little bit more repetition before sleeping”.

What is the difference between wiederholen, lernen, and English “revise/review”?

In this context:

wiederholen = to repeat / go over / review material you already learned.
lernen = to learn / study (not necessarily something you already know).

So:

Ich lerne neue Vokabeln. → I’m learning new vocabulary.
Ich wiederhole die Vokabeln. → I’m reviewing/revising the vocabulary.

English note:

In British English, “revise” for exams corresponds to wiederholen.
In American English, “review” is the usual word for that, also wiederholen.

So the sentence means: the notebook is there so I can review/go over stuff before bed, not so much “learn for the first time”.

Why is it noch etwas wiederholen and not etwas noch wiederholen?

Both word orders are technically possible, but the usual and most natural is:

noch etwas wiederholen = review a bit more / review something more.

In the middle field of a clause (between subject and verb-at-the-end), adverbs like noch usually come before indefinite pronouns like etwas:

Ich will noch etwas lesen.
Ich möchte noch etwas essen.

Etwas noch wiederholen would sound unusual and marked; it would put special emphasis on noch (something like “repeat it still / yet”), which doesn’t fit as well here. The sentence is just expressing “some more reviewing”, so noch etwas wiederholen is the standard word order.

Why is it immer after the verb: Mein Wörterheft liegt immer neben dem Bett?

In main clauses, German tends to keep:

Position 1: some element (often the subject)
Position 2: the conjugated verb
The rest of the elements (objects, adverbials, etc.)

Adverbs of frequency like immer (always), oft (often), selten (rarely), nie (never) usually come relatively early, often right after the verb:

Ich gehe immer um 7 Uhr ins Bett.
Er arbeitet oft abends.
Mein Wörterheft liegt immer neben dem Bett.

Other positions are possible (e.g. Immer liegt mein Wörterheft …) but that sounds more marked and stylistic. The given order is the most natural neutral statement.

What does Wörterheft mean exactly, and is Vokabelheft more common?

Wörterheft literally: “word notebook”.
Vokabelheft: “vocabulary notebook”, i.e. for foreign language vocabulary.

In practice:

For a foreign language learner, Vokabelheft is more common and specific.
Wörterheft is understood and correct, but a teacher or textbook might more typically say Vokabelheft.

So you could also say:

Mein Vokabelheft liegt immer neben dem Bett …
→ My vocabulary notebook always lies next to the bed …

Could I say beim Schlafen instead of vor dem Schlafen? What would change?

Yes, but the meaning changes:

vor dem Schlafen = before sleeping / before going to sleep
beim Schlafen = while sleeping / during sleep

Beim = bei dem and usually means “while doing X” with a nominalized infinitive:

Beim Essen höre ich Musik. → I listen to music while eating.
Beim Lernen trinke ich Kaffee. → I drink coffee while studying.

So:

… damit ich beim Schlafen noch etwas wiederholen kann
would mean “so that I can still review something while sleeping” – which doesn’t really make sense in a normal context.

Therefore vor dem Schlafen is the correct expression for “before going to sleep”.

Why is there a comma before damit?

In German, subordinate clauses introduced by conjunctions like dass, weil, obwohl, wenn, damit are almost always separated from the main clause with a comma.

Structure here:

Main clause: Mein Wörterheft liegt immer neben dem Bett,
Subordinate clause (purpose): damit ich vor dem Schlafen noch etwas wiederholen kann.

So:

The comma marks the beginning of the subordinate clause.
The verb at the end (kann) and the comma together clearly show that damit ich vor dem Schlafen noch etwas wiederholen kann is one whole dependent clause.