Звукорежиссёр проверил стойку для микрофона и микшер.

Both nouns are the direct objects of проверил (checked), so they are in the accusative case.

• стойка is a feminine noun, so in the accusative singular it changes:

  • nominative: стойка
  • accusative: стойку

• микшер is a masculine inanimate noun. For masculine inanimate nouns, the accusative singular is usually the same as the nominative:

  • nominative: микшер
  • accusative: микшер

So the sentence is grammatical as written:

• проверил стойку
• проверил микшер

The preposition для (for) requires the genitive case.

So:

• nominative: микрофон
• genitive: микрофона

That is why you get:

• стойка для микрофона = a stand for a microphone / mic stand

This is a very common pattern in Russian:

• чашка для чая = a cup for tea
• сумка для ноутбука = a bag for a laptop
• подставка для телефона = a stand for a phone

Yes. Literally, it means stand for a microphone, but in natural English that is usually microphone stand or mic stand.

Russian often expresses this idea with noun + для + genitive:

• стойка для микрофона
• literally: stand for microphone
• natural translation: microphone stand

You may also see микрофонная стойка, which is another way to say microphone stand.

Russian does not have articles like a, an, or the.

So:

• Звукорежиссёр can mean the sound engineer or a sound engineer
• микшер can mean the mixer or a mixer

The exact meaning depends on context. In many cases, Russian leaves that information unstated unless it is important.

Проверил is the perfective past form of проверить. It usually means the action was completed: checked, did a check of.

So this sentence presents the checking as a finished action:

• Звукорежиссёр проверил... = The sound engineer checked...

If you used проверял instead, that would be the imperfective past of проверять, and it would suggest:

• an ongoing process,
• repeated checking,
• or focus on the activity rather than the result.

Very roughly:

• проверил = checked, finished checking
• проверял = was checking / checked repeatedly / used to check

It is capitalized because it is the first word of the sentence, not because it is a job title.

In Russian, common nouns like звукорежиссёр are normally written with a lowercase letter unless they start a sentence.

So:

• Звукорежиссёр проверил микшер.
• but in the middle of a sentence: Я видел звукорежиссёра.

The stress is on the final ё:

• звукорежиссёр

That ё is important, because ё is always stressed when written.

A rough pronunciation guide:

• zvu-ka-re-zhi-SYOR

A few helpful points:

• зв at the start can feel difficult for English speakers
• ж sounds like the s in measure
• ё sounds roughly like yo, but here after a consonant it gives -syor / -syor depending on how you hear it

Also, in normal printed Russian, ё is sometimes replaced by е, so you may see:

• звукорежиссер

But the pronunciation and stress are still:

• звукорежиссёр

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

The neutral order here is:

• subject + verb + object
• Звукорежиссёр проверил стойку для микрофона и микшер.

But other orders are possible if you want different emphasis, for example:

• Микшер и стойку для микрофона проверил звукорежиссёр.
• Стойку для микрофона и микшер звукорежиссёр проверил.

These alternatives change emphasis or sound more marked. The original sentence is the most straightforward and neutral.

Yes. This is completely normal.

The verb проверил applies to both objects:

• стойку для микрофона
• микшер

So the structure is basically:

• checked [the mic stand] and [the mixer]

Russian, like English, does not need to repeat the verb:

• The sound engineer checked the microphone stand and the mixer.

Here микшер means an audio mixer / mixing console / mixer, depending on context.

Because the sentence is about a звукорежиссёр (sound engineer), the audio meaning is the natural one.

In other contexts, миксер with one ш/с difference is a different word:

• миксер = usually a kitchen mixer or hand mixer
• микшер = more often a technical/audio mixing device

So in this sentence, микшер is the sound equipment.

Yes, it is one word.

It is made from:

• звук = sound
• режиссёр = director

So literally it is something like sound director, but the normal English translation is:

• sound engineer
• sometimes audio engineer, depending on context

This is a good example of a Russian compound noun that has a natural English equivalent rather than a word-for-word translation.