Дочка выучила стихотворение наизусть и потом прочитала его бабушке.

Both mean daughter, but дочка is the more everyday, warm, natural-sounding word here. It often feels a little more affectionate. Дочь is more neutral and can sound more formal or literary in some contexts.

So:

• дочка = daughter, more colloquial/affectionate
• дочь = daughter, more neutral/formal

In ordinary family-style narration, дочка is very common.

In the past tense, Russian verbs agree with the subject in gender and number.

The subject is дочка, which is feminine singular, so the past-tense verbs are also feminine singular:

• выучил = he learned/memorized
• выучила = she learned/memorized
• прочитал = he read
• прочитала = she read

If the subject were сын or мальчик, you would get выучил and прочитал.

This is about aspect.

• учить / учила is imperfective: it describes the process, repetition, or an unfinished action.
• выучить / выучила is perfective: it means she learned it successfully, to completion.

Here the idea is not just that she spent time studying the poem, but that she memorized it completely. So выучила is the natural choice.

Compare:

• Дочка учила стихотворение. = The daughter was learning/studying the poem.
• Дочка выучила стихотворение. = The daughter learned/memorized the poem completely.

Наизусть means by heart, from memory.

So выучила стихотворение наизусть means she memorized the poem so she could say it without looking at a text.

It is a fixed adverb, and it is written as one word:

• наизусть

Common combinations include:

• учить наизусть = to learn by heart
• знать наизусть = to know by heart
• читать наизусть = to recite from memory

Because it is a direct object in the accusative case, and for many inanimate neuter nouns, the accusative singular looks exactly the same as the nominative singular.

So:

• nominative: стихотворение
• accusative: стихотворение

That is why the form does not change.

Because его is the form needed for the direct object here.

The pronoun refers to стихотворение = it. After прочитала, Russian needs the object form, not the subject form.

• оно = it in the nominative case
• его = it in the accusative/genitive form

So:

• Оно длинное. = It is long.
• Она прочитала его. = She read it.

In this sentence, его means the poem, not him.

Because бабушке is dative singular. It marks the recipient or the person to whom something is read.

The verb pattern is:

• прочитать что? кому?
• read what? to whom?

So:

• его = what was read
• бабушке = to whom it was read

Base form:

• бабушка = grandmother

Dative singular:

• бабушке = to grandmother / to grandma

Because Russian often uses the dative case by itself to express to someone after certain verbs.

With verbs like дать, показать, рассказать, прочитать, the person receiving something is commonly in the dative without a preposition:

• дать маме книгу = give Mom a book
• показать другу фото = show a friend a photo
• прочитать бабушке стихотворение = read Grandma a poem / read a poem to Grandma

So English needs to, but Russian often does not.

Потом by itself means then / afterwards / later.
И means and.

Together, и потом gives the flow and then. It links the two actions and makes the sequence very clear:

1. she memorized the poem
2. and then she read it to Grandma

You could sometimes say just потом, but и потом is very natural in storytelling.

Yes, Russian word order is fairly flexible.

This version is natural because:

• его refers to something already mentioned, so the short pronoun comes early
• бабушке comes after it as the recipient

But other orders are possible, depending on emphasis:

• Дочка выучила стихотворение наизусть и потом прочитала бабушке его.
• Дочка выучила стихотворение наизусть и потом бабушке его прочитала.
• Потом дочка прочитала его бабушке.

The original order is simply a smooth, neutral way to say it.

No, because the cases make the roles clear.

• его is the direct object: the thing being read
• бабушке is dative: the person listening / receiving the reading

So the structure is:

• read it to Grandma

not

• read Grandma

Russian case endings do a lot of work that English often does with word order or prepositions.