Когда кошка сыта и спокойна, она ложится рядом и громко мурлычет.

Here когда can be understood as when or whenever.

Because the sentence is in the present tense and describes a typical pattern of behavior, the sense is:

Whenever the cat is full and calm, it lies down nearby and purrs loudly.

So this is not just one specific moment; it is a general statement. Russian often uses когда this way.

If you used если, the sentence would sound more like a condition or hypothesis: if the cat is full and calm...
With когда, the idea is more this is what happens when that situation occurs.

Because сыта and спокойна are short-form adjectives, which are commonly used in Russian as part of the predicate:

• кошка сыта = the cat is full
• кошка спокойна = the cat is calm

By contrast, the full forms сытая and спокойная are more naturally used to describe the noun itself:

• сытая кошка = a full cat
• спокойная кошка = a calm cat

So:

• сытая кошка describes what kind of cat
• кошка сыта describes the cat’s current state

That is why the short forms are natural here.

Yes. In present-tense Russian, the verb to be is usually omitted.

So:

• кошка сыта и спокойна literally means the cat [is] full and calm

This is completely normal.

Compare:

• present: кошка сыта
• past: кошка была сыта
• future: кошка будет сыта

So the English is is understood, not spoken.

Because they agree with кошка, which is feminine singular.

Short-form adjectives still agree in gender and number:

• сыт — masculine
• сыта — feminine
• сыто — neuter
• сыты — plural

And similarly:

• спокоен — masculine
• спокойна — feminine
• спокойно — neuter
• спокойны — plural

Since кошка is feminine, the sentence needs сыта and спокойна.

These two verbs are related, but they are not the same:

• ложиться = to lie down, to settle oneself down
• лежать = to be lying, to be in a lying position

So:

• она ложится рядом = she lies down nearby
• она лежит рядом = she is lying nearby

The sentence uses ложится because it presents the action of the cat settling down. If you used лежит, the focus would be on the state after that action.

It describes a habitual / repeated action.

Russian present tense is often used for things that happen regularly:

• Когда кошка сыта и спокойна, она ложится рядом и громко мурлычет.

This means something like:

When/whenever the cat is full and calm, this is what it does.

Also, ложиться is imperfective, which fits repeated or ongoing behavior well.

If you wanted a single future event, Russian would normally use a different form, for example:

• Когда кошка будет сыта и спокойна, она ляжет рядом...

Here ляжет is the perfective future form of лечь.

In this sentence, она is natural and expected.

Russian can sometimes omit pronouns, but not as freely as some other languages. After the opening clause Когда кошка сыта и спокойна, the pronoun она clearly starts the main clause again:

• Когда кошка сыта и спокойна, она ложится рядом...

Without она, the sentence would sound much less natural as a standalone example.

So even though the cat has already been mentioned, repeating it as она helps make the structure clear.

Here рядом means nearby or close by.

It can be used in two ways:

1. On its own, as an adverb

   • она ложится рядом = she lies down nearby

2. With с + instrumental, to say next to whom or what

   • она ложится рядом с хозяином = she lies down next to her owner

So in your sentence, the reference point is simply left understood.

Because громко is an adverb, and it modifies the verb мурлычет.

• громко мурлычет = purrs loudly

Adjectives modify nouns:

• громкое мурлыканье = loud purring

So:

• громкая would need a feminine noun
• громко is the correct form to describe how the cat purrs

A very common Russian pattern is:

• adjective: громкий
• adverb: громко

Because Когда кошка сыта и спокойна is a subordinate clause introduced by когда.

In Russian, subordinate clauses are normally separated from the main clause by a comma:

• Когда кошка сыта и спокойна, она ложится рядом и громко мурлычет.

This is the standard punctuation rule.

Russian word order is fairly flexible, but the version in the sentence is neutral and natural.

For example:

• она ложится рядом и громко мурлычет
• она ложится рядом и мурлычет громко

Both are possible, but they place the emphasis slightly differently.

The given order sounds smooth and straightforward: first the cat lies down, then we are told that it purrs, and громко naturally describes the manner of purring.

So the word order is not completely fixed, but the original sentence is a very normal way to say it.