Мой кот лежит на диване и мурлычет.

Because кот is a masculine singular noun, and мой has to agree with it.

In Russian, possessive words like мой change for gender, number, and case:

• мой кот = my cat, masculine
• моя кошка = my cat, feminine
• моё окно = my window, neuter
• мои коты = my cats, plural

Here, кот is masculine, so мой is the correct form.

Strictly speaking, кот usually means a male cat.

Compare:

• кот = male cat / tomcat
• кошка = female cat
• кошка can also sometimes be used more generally for cat as a species

So мой кот suggests that the speaker has a male cat. If the cat were female, you would normally say моя кошка.

Лежит is the 3rd person singular present tense of лежать.

So:

• лежать = to lie, to be lying
• лежит = he/she/it lies, is lying

It matches кот because кот is:

• 3rd person
• singular

This verb is used for something in a horizontal position, so it fits a cat lying on a sofa.

Russian does not build the present continuous the way English does.

In English, you say:

• lies
• is lying

In Russian, one present-tense verb often covers both ideas:

• лежит = lies / is lying
• мурлычет = purrs / is purring

So Мой кот лежит на диване и мурлычет can naturally mean My cat is lying on the sofa and purring.

There is no separate present-tense auxiliary like English is here.

Because this sentence describes location, not movement.

With на, Russian often distinguishes:

• куда? = where to? → accusative
• где? = where? → prepositional

So:

• на диван = onto the sofa
• на диване = on the sofa

Here the cat is already there, so Russian uses the prepositional case:

• диван → на диване

Диване is in the prepositional singular.

The basic form is:

• диван = sofa

After на when it means on in the sense of location, Russian uses the prepositional:

• на диване = on the sofa

For many masculine nouns, that means adding -е:

• стол → на столе
• диван → на диване

So the ending -е tells you the noun is in the prepositional case.

Мурлычет is the 3rd person singular present tense of мурлыкать.

So:

• мурлыкать = to purr
• мурлычет = he/she/it purrs, is purring

Like лежит, it agrees with кот, which is singular.

One thing learners often notice is that the stem changes a little:

• мурлыка- → мурлыч-

That kind of consonant change is normal in Russian verb conjugation.

Because the subject is still the same: мой кот.

Russian, like English, usually does not repeat the subject when two verbs share it:

• Мой кот лежит на диване и мурлычет.

This means:

• My cat is lying on the sofa and purring.

You could say и он мурлычет, but that would sound more marked and would usually add emphasis or contrast. The version without он is the most natural neutral sentence.

Yes. Russian word order is more flexible than English word order.

The version here is the most neutral:

• Мой кот лежит на диване и мурлычет.

If you change the order, the basic meaning can stay the same, but the emphasis changes. For example:

• На диване лежит мой кот и мурлычет.
  This puts more focus on where the cat is.

Russian uses case endings to show grammatical relationships, so word order is often used for emphasis, topic, or style rather than basic grammar alone.

The stressed syllables are:

Мой кот лежи́т на дива́не и мурлы́чет.

A rough English-style approximation is:

moy kot lye-ZHEET na dee-VA-nye ee moor-LY-chet

A few helpful notes:

• лежит has stress on the last syllable: -жи́т
• диване has stress on ва́
• мурлычет has stress on лы́
• диване is pronounced more like dee-VA-nye, not di-va-ne

If you want to sound more natural, the stress is more important than making every vowel sound exactly like English.

Yes, if the context already makes it clear whose cat it is.

For example:

• Кот лежит на диване и мурлычет. = The cat is lying on the sofa and purring.

Adding мой makes it explicit:

• Мой кот... = my cat...

So мой is not grammatically required for the sentence structure, but it is required if you want to specifically say my cat.