Моя дочка сама засыпает в кроватке.

Because дочка is a feminine noun, and the possessive my has to agree with it in gender.

• masculine: мой
• feminine: моя
• neuter: моё
• plural: мои

So:

• мой сын = my son
• моя дочка = my daughter

In this sentence, моя is nominative feminine singular to match дочка.

Дочь is the basic word for daughter.

Дочка is a very common diminutive / affectionate form. It often sounds warmer, more personal, or more natural in everyday family speech.

So:

• дочь = daughter
• дочка = daughter / little daughter / dear daughter

It does not always mean the daughter is very young; it often just adds affection.

Сама means by herself / on her own here.

It is the feminine form of сам, which is used for emphasis. It agrees with дочка, so it must also be feminine:

• сам = masculine
• сама = feminine
• само = neuter
• сами = plural

So Моя дочка сама засыпает means that the daughter falls asleep without help, without someone putting her to sleep, or on her own.

It is not just a literal herself in the English reflexive sense. In this kind of sentence, it usually emphasizes independence.

Because засыпать means to fall asleep / to go to sleep, while спать means to sleep.

So there is an important difference:

• спит = is sleeping
• засыпает = falls asleep / is falling asleep / goes to sleep

In your sentence, the meaning is about the process of getting to sleep, not the state of already being asleep.

Засыпает is 3rd person singular present tense of засыпать.

In Russian, the present tense of an imperfective verb is often used for:

• habitual actions
• repeated actions
• general facts

So Моя дочка сама засыпает в кроватке usually means something like:

• My daughter falls asleep on her own in her crib
• My daughter goes to sleep on her own in her crib

It sounds like a regular habit, not necessarily something happening only right now.

Засыпать is imperfective.

Its common perfective partner is заснуть.

• засыпать = to be falling asleep / to fall asleep habitually
• заснуть = to fall asleep once, as a completed event

Examples:

• Она обычно быстро засыпает. = She usually falls asleep quickly.
• Она наконец заснула. = She finally fell asleep.

In your sentence, the imperfective makes sense because it describes a usual pattern.

В кроватке is in the prepositional case because в is being used to mean in a location.

Here, the idea is where the daughter falls asleep:

• в кроватке = in the little bed / in the crib

The dictionary form is кроватка. In the prepositional singular, it becomes кроватке.

So:

• nominative: кроватка
• prepositional: в кроватке

Кровать is the basic word for bed.

Кроватка is a diminutive form. It often means:

• little bed
• crib
• cot
• or just a more affectionate way of saying bed

In a sentence about a small child, в кроватке very naturally suggests in the crib or in her little bed.

Yes, Russian word order is fairly flexible.

This order is natural and neutral:

• Моя дочка сама засыпает в кроватке.

It presents the subject first, then the emphasis on сама, then the verb, then the location.

You could rearrange it, but the emphasis would change. For example:

• Моя дочка в кроватке сама засыпает.
  Slightly more emphasis on the location or contrast in context.

• Сама моя дочка засыпает в кроватке.
  This sounds more marked and would usually need a special context.

For learners, the original order is a very good default.

Yes, it often can be omitted if the context already makes it obvious whose daughter is being discussed.

For example:

• Дочка сама засыпает в кроватке.

This can still mean My daughter falls asleep on her own in her crib, depending on context.

Russian often leaves out possessives when ownership or relationship is already clear. But моя can be included for clarity, contrast, or emphasis.

Yes, grammatically you can.

But the tone changes:

• дочь sounds more neutral, standard, sometimes a bit less warm
• дочка sounds more natural in family speech and more affectionate

With a sentence about a small child and a crib, дочка fits especially well.

Because the ending -ет here marks 3rd person singular in the present tense for this verb pattern.

The infinitive is засыпать. Its present-tense forms are:

• я засыпаю = I fall asleep
• ты засыпаешь = you fall asleep
• он / она засыпает = he / she falls asleep
• мы засыпаем
• вы засыпаете
• они засыпают

Since the subject is моя дочка, the verb must be засыпает.

The standard stresses are:

• моя́
• до́чка
• сама́
• засыпа́ет
• в крова́тке

So the full sentence is pronounced:

моя́ до́чка сама́ засыпа́ет в крова́тке

Stress is very important in Russian, because it is not always predictable from spelling.