Прогрессивные линзы подходят при дальнозоркости.

Because it is an adjective agreeing with линзы.

• линзы is plural
• it is in the nominative case here, because it is the subject of the sentence
• so the adjective must also be plural nominative

That gives:

• singular masculine: прогрессивный
• singular feminine: прогрессивная
• singular neuter: прогрессивное
• plural: прогрессивные

So прогрессивные линзы = progressive lenses.

Because the sentence is talking about lenses in general, not one single lens.

In Russian, as in English, this idea is often naturally expressed in the plural:

• линза = a lens
• линзы = lenses

Also, the standard term for progressive lenses is normally used in the plural: прогрессивные линзы.

Because it agrees with the subject прогрессивные линзы, which is plural.

Compare:

• Линза подходит. = The lens is suitable.
• Линзы подходят. = The lenses are suitable.

So подходят is the 3rd person plural form of подходить.

Here подходят means something like:

• are suitable
• work well
• are appropriate
• are a good option

It does not literally mean physical movement here, even though подходить can also mean to approach / come up to in other contexts.

In this sentence, the meaning is about suitability:

• Эти очки подходят мне. = These glasses suit me / are good for me.
• Прогрессивные линзы подходят при дальнозоркости. = Progressive lenses are suitable for farsightedness.

Дальнозоркости is in the prepositional case because it follows the preposition при.

The noun is:

• дальнозоркость = farsightedness

Its prepositional singular form is:

• при дальнозоркости

In medical or formal language, при + prepositional often means:

• in cases of
• when there is
• with

So:

• при дальнозоркости = in cases of farsightedness / for farsightedness

Not exactly.

Both can sometimes be translated with for, but the nuance is different.

• при дальнозоркости = in cases of farsightedness / when someone has farsightedness
• для дальнозоркости would sound less natural in this medical statement

In medical and instructional language, при is very common when talking about a condition or circumstance:

• при простуде = when you have a cold
• при беременности = during pregnancy / in pregnancy
• при дальнозоркости = in cases of farsightedness

So при дальнозоркости is the most natural choice here.

Because Russian does not normally use a separate present-tense form of to be like English does.

In English:

• Progressive lenses are suitable...

In Russian, the verb подходят already carries the meaning of the predicate, so no extra are is needed.

Russian often leaves out to be in the present tense:

• Он врач. = He is a doctor.
• Это интересно. = This is interesting.

But in your sentence, the main verb is not to be anyway — it is подходят = are suitable / suit.

Yes, it is a standard term for progressive lenses.

Even though прогрессивный can mean progressive in many contexts, here it is part of an established optical term:

• прогрессивные линзы = progressive lenses

So this is normal vocabulary, not an unusual literal translation.

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

The sentence as written:

• Прогрессивные линзы подходят при дальнозоркости.

is neutral and natural.

You could also say:

• При дальнозоркости подходят прогрессивные линзы.

This puts more focus on the condition при дальнозоркости.

But the original order is probably the clearest default version for a learner.

Yes, it sounds somewhat informational, neutral, and a bit medical/optical.

That is mainly because of:

• подходят = a neutral way to say something is suitable
• при дальнозоркости = a common formal/medical pattern

In everyday conversation, someone might also say something more personal, for example:

• При дальнозоркости такие линзы могут хорошо подойти.
• Если у вас дальнозоркость, прогрессивные линзы могут быть удобны.

But the original sentence is perfectly natural in a medical, optical, or explanatory context.

The dictionary form is дальнозоркость.

This is a feminine noun ending in -ость, and nouns of this type are often abstract nouns, like English nouns ending in -ness or -ity.

Examples:

• скорость = speed
• молодость = youth
• близорукость = nearsightedness
• дальнозоркость = farsightedness

Its forms include:

• nominative: дальнозоркость
• prepositional: о дальнозоркости, при дальнозоркости

So in your sentence, дальнозоркости is just the expected prepositional form.

The main stress is:

• прогресси́вные ли́нзы подхо́дят при дальнозо́ркости

A rough pronunciation guide:

• прогресси́вные = prah-gree-SEEv-ny-ye
• ли́нзы = LEEN-zy
• подхо́дят = paht-KHO-dyat
• при = pree
• дальнозо́ркости = dal-na-ZOR-ka-stee

For a learner, the most useful thing is probably to remember the stressed syllables:

• -си́в-
• ли́н-
• -хо́-
• -зо́р-

Those stresses will help you sound much more natural.