Перемикач передач рухається повільно.

Because перемикач передач is built like shifter of gears.

• перемикач = switch / shifter
• передач = genitive plural of передача

In Ukrainian, the second noun in this kind of phrase often goes into the genitive case: X of Y. So перемикач передач literally means shifter of gears. The plural is natural because a gear shifter is connected with the set of gears in general, not just one gear.

Yes, in car-related context it can.

The noun передача has several meanings depending on context, including:

• transfer / transmission
• broadcast / TV program
• gear (in a vehicle)

Here, because it follows перемикач and the meaning is about a vehicle, передач clearly means gears.

Рухається is the 3rd person singular present tense form of рухатися.

That means it agrees with перемикач, which is singular:

• перемикач ... рухається = the gear shifter moves / is moving

If the subject were plural, the verb would change too:

• перемикачі ... рухаються = the shifters move / are moving

The -ся marks the verb as a reflexive/intransitive form.

In this sentence, it does not mean the gear shifter is literally moving itself in a dramatic English sense. It is just the normal Ukrainian verb form for to move in this kind of usage.

A helpful contrast is:

• рухати = to move something
• рухатися = to move

So рухається means moves / is moving.

Because повільно is an adverb, and the sentence needs an adverb here.

• повільний = slow (adjective, describes a noun)
• повільно = slowly (adverb, describes a verb)

Here it describes how the gear shifter moves:

• рухається повільно = moves slowly

If you said повільний перемикач, that would mean a slow gear shifter.

It can mean either, depending on context.

Ukrainian present tense often covers both:

• simple present: moves slowly
• present continuous: is moving slowly

So without extra context, this sentence could be translated either way in English.

Yes. Ukrainian word order is fairly flexible.

The version you have, Перемикач передач рухається повільно, is neutral and natural.

You could also say:

• Перемикач передач повільно рухається — also natural
• Повільно рухається перемикач передач — stronger emphasis on slowly

Because Ukrainian uses endings to show grammatical relationships, word order is often used for emphasis rather than basic grammar.

A rough English-friendly approximation is roo-KHA-ye-tsya.

A few details:

• ру sounds like roo
• х is a throat sound, like ch in Scottish loch or German Bach
• ає here gives a a-ye kind of sequence
• -ться / -ється is usually pronounced quickly, roughly like -tsya / -yetsya

So рухається is not pronounced like an English g sound anywhere; the tricky part is really the х and the quick -ється ending.

Because Ukrainian has no articles.

So Ukrainian does not have separate words for a / an / the. Whether English should use a gear shifter or the gear shifter depends on context, not on a special Ukrainian word.

That means Перемикач передач рухається повільно can correspond to:

• The gear shifter moves slowly
• A gear shifter moves slowly

Context tells you which one is meant.