تخرخر القطة ويتحرك ذيلها.

Because القطة is grammatically feminine singular. In the present tense, Arabic uses تـ for the third-person feminine singular form.

So:

• تخرخر القطة = the cat purrs
• but يخرخر القط = the male cat purrs

In other words, the verb agrees with القطة in gender and number.

Mostly both, depending on context.

• قطة is the feminine form of the noun.
• It can mean female cat specifically.
• But in many simple learning sentences, it is also just used as the normal word for cat.

If you specifically wanted male cat, you would usually say قط.

So in this sentence, القطة is treated as feminine, and that is why the verb is تخرخر.

Because the subject of the second verb is ذيل (tail), not القطة.

• ذيل is grammatically masculine singular.
• So the verb must be masculine singular: يتحرك
• ها only means her/its and shows possession; it does not make the subject feminine.

So:

• يتحرك ذيلها = her/its tail moves

If the subject were a feminine noun, then you would use تتحرك instead.

It breaks down like this:

• ذيل = tail
• ها = her / its

So literally it is tail-her, which in natural English becomes her tail or its tail.

Arabic often shows possession by attaching a pronoun directly to the noun.

Because a noun with an attached pronoun is already definite.

• ذيل = a tail / tail
• ذيلها = her tail / its tail

Once the suffix ها is attached, the noun is automatically definite, so you do not add ال.

So الذيلها would be wrong.

و means and.

It connects the two parts of the sentence:

• تخرخر القطة = the cat purrs
• ويتحرك ذيلها = and its tail moves

In Arabic writing, و is attached directly to the next word.

Yes. In Modern Standard Arabic, it is very common for the verb to come first.

So this sentence uses a normal verbal word order:

• تخرخر القطة
• يتحرك ذيلها

But Arabic can also use subject-first order. For example:

• القطة تخرخر وذيلها يتحرك

That is also correct. The meaning is basically the same, though the emphasis or flow can feel a little different.

Yes, in a sense. Arabic verbs already contain subject information, so an independent pronoun is usually unnecessary.

For example:

• تخرخر already tells you she/it is doing the action
• يتحرك already tells you he/it is doing the action

So Arabic normally does not need to say هي before تخرخر.

Once the noun appears, as in تخرخر القطة, that noun is understood as the subject.

They are both in the nominative case because they are the subjects of their verbs.

In fully vocalized MSA, you would write:

• القطةُ
• ذيلُها

So the fully vocalized sentence is:

تُخَرْخِرُ القِطَّةُ وَيَتَحَرَّكُ ذَيْلُهَا.

In normal everyday writing, those short final vowels are usually left unwritten.

It can mean either, depending on context.

The Arabic present tense (المضارع) often covers both:

• simple present: The cat purrs
• present progressive: The cat is purring

So this sentence could describe a general fact or something happening right now. Context tells you which meaning is intended.

If you wanted to make right now clearer, you could add a word like الآن (now).

With full vowels, it is:

تُخَرْخِرُ القِطَّةُ وَيَتَحَرَّكُ ذَيْلُهَا

A helpful transliteration is:

tukharkhiru al-qiṭṭatu wa-yataḥarraku dhayluhā

A few sound notes:

• خ is the kh sound, like the ch in German Bach
• ق is a deep q sound, farther back than English k
• ط is an emphatic t

So the first word تخرخر has a repeated, rumbling shape that fits the idea of purring.