Optyk pokazuje sposób badania wzroku.

Optyk is in the nominative singular. It is the subject of the sentence — the person who performs the action.

• optyk = optician / eye specialist in this context
• It answers the question who shows? → optyk

Because Polish uses case endings, the subject is usually in the nominative.

Pokazuje is the 3rd person singular present tense form of pokazywać (to show, imperfective).

It matches the subject optyk, which is singular:

• ja pokazuję = I show
• ty pokazujesz = you show
• on/ona pokazuje = he/she shows

Here it means something like:

• shows
• is showing
• demonstrates

Because Polish present tense can cover both a simple present and an ongoing present, the exact English wording depends on context.

Because sposób is the direct object of pokazuje, so it is in the accusative case.

For many masculine inanimate nouns, the accusative singular looks exactly like the nominative singular:

• nominative: sposób
• accusative: sposób

So even though it is the object, the form does not change.

Here badania is not plural. It is the genitive singular of badanie.

The noun changes like this:

• nominative singular: badanie = examination / testing
• genitive singular: badania = of examination / of testing

In this sentence, sposób badania wzroku means the method/way of testing eyesight.

So badania is singular, even though it may look plural to a learner.

Because sposób is often followed by a noun in the genitive to mean the way/method of doing something.

So:

• sposób badania = the method of examining / the way of testing
• sposób nauki = the method of learning
• sposób rozwiązania problemu = the way of solving the problem

This is a very common Polish pattern:

• noun + genitive noun
  to express of ...

Wzroku is the genitive singular of wzrok (eyesight, vision).

It appears here because badanie wzroku is a standard Polish expression meaning:

• eyesight test
• vision test
• literally: examination of eyesight

So the structure is:

• sposób → method
• badania → of examination/testing
• wzroku → of eyesight

This creates a chain of nouns: sposób badania wzroku = the method of testing eyesight

Wzrok means eyesight / vision, while oczy means eyes.

So:

• badanie wzroku = testing vision/eyesight
• badanie oczu = examination of the eyes themselves

In many medical or optical contexts, badanie wzroku is the normal phrase for an eye test at the optician’s or optometrist’s.

Yes, this word order is fairly neutral:

Optyk pokazuje sposób badania wzroku.

Polish word order is flexible because cases show grammatical roles. So you can change the order for emphasis:

• Sposób badania wzroku pokazuje optyk.
  → emphasizes the method

• Badania wzroku sposób pokazuje optyk.
  → grammatically possible in poetry or very marked speech, but not natural in normal conversation

The most natural order here is the original one: subject + verb + object.

Because Polish has no articles.

So optyk can mean:

• the optician
• an optician

and sposób can mean:

• the method
• a method

Context tells you which one is meant. This is normal in Polish.

Yes, it is grammatical and understandable. It sounds a bit formal or instruction-like, because it uses a noun-heavy structure:

sposób badania wzroku = the method of eyesight testing

In everyday speech, a Pole might also say something more conversational, such as:

• Optyk pokazuje, jak bada się wzrok.
  = The optician shows how eyesight is tested.

• Optyk pokazuje, jak wygląda badanie wzroku.
  = The optician shows what an eyesight test looks like.

So the original sentence is fine, but slightly more formal in style.

Yes. Pokazuje comes from the imperfective verb pokazywać.

That suggests:

• an ongoing action
• a repeated action
• a general/habitual fact

So it can mean:

• is showing
• shows
• demonstrates

If you wanted a completed, one-time action, Polish would usually use the perfective verb pokazać:

• Optyk pokaże sposób badania wzroku. = The optician will show the method of testing eyesight.
• Optyk pokazał sposób badania wzroku. = The optician showed the method of testing eyesight.

So yes, aspect matters, and the original sentence uses the imperfective.