Learn Hardcore Russian: Для меня невозможно уснуть без книги: я держу её в руках, пока не закрою глаза. - It is impossible for me to fall asleep without a book: I hold it in my hands until I close my eyes.

Для меня невозможно + infinitive literally means “for me, it is impossible to …” and is idiomatic. It frames the statement as a personal condition or perspective.
Мне невозможно уснуть is also possible; using the dative (мне) makes it feel a bit more like a personal experience affecting you.
The most everyday way to say it is Я не могу уснуть без книги (“I can’t fall asleep without a book”).
Another very natural option is the impersonal: Мне не заснуть без книги (“I can’t get to sleep without a book”).

What case is меня after для, and why?

Для always takes the genitive case, so меня is genitive singular. Patterns: для меня, для тебя, для него/неё, для нас, для вас, для них.

Why невозможно and not нельзя or трудно?

Невозможно = “impossible” (cannot be done).
Нельзя often means “not allowed” or “must not,” though it can also mean “cannot” in some contexts; here it might sound like a rule rather than a personal inability.
Трудно/сложно = “hard/difficult,” weaker than “impossible.” For a personal inability, невозможно, не могу, or мне не заснуть are the best choices.

Why is уснуть used instead of спать or засыпать? What about заснуть?

Спать = “to sleep” (state), not the transition into sleep.
Уснуть and заснуть are both perfective “to fall asleep.” Both fit here; заснуть is very common, уснуть is also standard (slightly more formal/bookish).
The imperfective partner for the process/habit is засыпать (“to be falling asleep,” or “to fall asleep” habitually).

Why is there a colon before я держу её…? Could I use a period or a dash?

The colon introduces an explanation of the first clause: “It’s impossible for me to fall asleep without a book: I hold it…” A period would also work; a dash is possible for a more dramatic pause. All three are acceptable with slightly different tones.

Why is её used for “book”? Isn’t that “her”?

Russian pronouns agree with grammatical gender. Книга is feminine, so the pronoun referring to it is её (“her/it” for feminine nouns). Here её means “it,” referring to книга. Note: you’ll often see it written as ее in print (without the two dots), but the pronunciation is the same.

What case is её here?

Accusative singular (direct object of держу). For feminine pronouns, accusative and genitive look the same: её.

Where does держу come from, and why not держаю?

It’s the 1st person singular present of держать (“to hold”): я держу, ты держишь, он/она держит, мы держим, вы держите, они держат. The correct 1sg form is держу (not держаю). Stress: держу́.

Why в руках and not на руках?

Держать в руках = “to hold in (one’s) hands” (a book, a phone, etc.).
На руках = “in one’s arms/being carried” (typically a child, a pet, or a person).

Why is руках plural? Could I say в руке?

The idiom is usually plural: держать в руках (“hold in (both) hands”). You can say в руке if you specifically mean “in one hand.” Both are correct; the plural is more generic/natural here.

What case is руках, and why does в take that case here?

В руках is prepositional plural of рука. With static location (“in/at/on somewhere”), в takes the prepositional case; with motion into, в takes the accusative.

Why is there a comma before пока?

Пока (не)… introduces a subordinate clause of time, so Russian punctuation requires a comma to separate it from the main clause: …, пока не закрою глаза.

Why does пока не have не if the meaning is “until,” not a negation?

In Russian, “until” is expressed by пока не + perfective verb. The не is obligatory in this construction and does not negate the meaning. Without не (пока) means “while/as long as.”

Why закрою (future perfective) after пока не? Why not present?

With пока не, Russian uses the perfective future to mark the endpoint event: “I keep holding it … until I close my eyes (i.e., at the moment of closing).” Even for a habitual description in the present, the boundary event appears as perfective future: держу … пока не закрою. Using закрываю would imply an ongoing process and is not idiomatic here.

What form is глаза?

Accusative plural (direct object of закрою). For inanimate masculine nouns, nominative and accusative plurals coincide, and глаза́ is also the irregular plural of глаз (“eye”). Stress: глаза́.

Can I drop её and just say я держу в руках, пока…?

Normally no—you need an object for держу. You can repeat the noun (держу книгу в руках) or keep the pronoun (держу её в руках). Omitting it entirely sounds incomplete unless the object is extremely obvious from context (and even then, Russian typically keeps it).

What are some very natural alternative ways to say the whole sentence?

Я не могу уснуть без книги: держу её в руках, пока не закрою глаза.
Мне не заснуть без книги: держу её в руках, пока не закрою глаза.
More colloquial/habitual: Я всегда засыпаю с книгой в руках.

Any quick pronunciation/stress tips for the key words?

невозмо́жно, усну́ть, кни́ги, держу́, её, в рука́х, пока́, закро́ю, глаза́.