Je kancelářská židle nastavená tak, aby byla pohodlná?

Because this is a yes/no question. In Czech, one common way to form a yes/no question is simply to put the verb first.

• Je kancelářská židle nastavená... = Is the office chair adjusted... ?

This is similar to English Is the chair... ?

A statement would normally be:

• Kancelářská židle je nastavená tak, aby byla pohodlná.
  = The office chair is adjusted so that it is comfortable.

So the initial Je signals that the speaker is asking a question.

Both words are in the nominative singular, because kancelářská židle is the subject of the sentence.

• židle = chair
• kancelářská = office / office-related

The adjective kancelářská has to agree with židle, which is:

• feminine
• singular
• nominative

So:

• kancelářský = masculine base form
• kancelářská = feminine nominative singular form

That is why you get kancelářská židle.

Nastavená agrees with židle, which is a feminine singular noun.

The adjective/participle nastavený changes form depending on gender and number:

• nastavený = masculine singular
• nastavená = feminine singular
• nastavené = neuter singular / plural in some contexts

Since židle is feminine, Czech uses:

• židle je nastavená = the chair is adjusted/set

So the ending -á is there because of grammatical agreement.

It is a past passive participle used in an adjective-like way.

In this sentence, je nastavená works much like English is adjusted or is set.

So you can think of it as:

• a verb-related form because it comes from nastavit = to set / adjust
• but it behaves like an adjective because it agrees with the noun in gender and number

That is very common in Czech.

So:

• židle je nastavená = literally something like the chair is adjusted/set

Tak, aby means something like:

• so that
• in such a way that
• so as to

In this sentence:

• Je kancelářská židle nastavená tak, aby byla pohodlná?
  = Is the office chair adjusted so that it is comfortable?

Here is the structure:

• tak = so / in such a way
• aby = introduces the intended result or purpose

This combination is very common in Czech when talking about the way something is arranged in order to achieve a result.

Examples:

• Sedni si tak, aby ses cítil pohodlně.
  = Sit in such a way that you feel comfortable.
• Nastav to tak, aby to fungovalo.
  = Set it so that it works.

After aby, Czech uses a special kind of verb form that expresses purpose, intention, or desired result. English often uses so that for this.

So:

• aby byla pohodlná = so that it would be comfortable / so that it is comfortable

The form byla here is based on the past-tense participle, but after aby it does not mean ordinary past time. It is part of the construction used after aby.

Also, pohodlná is an adjective, so Czech still needs the verb být (to be):

• byla pohodlná = be comfortable / be in a comfortable state

You cannot say aby je pohodlná, because that is not how Czech forms this kind of clause.

Because byla agrees with the subject of the subordinate clause, which is again židle.

Židle is:

• feminine
• singular

So the form is:

• byl = masculine singular
• byla = feminine singular
• bylo = neuter singular

That is why Czech says:

• aby byla pohodlná

If the noun were masculine, you would get something else, for example:

• stůl je nastavený tak, aby byl stabilní
  = the table is set so that it is stable

Because pohodlná agrees with židle, just like nastavená does.

The adjective pohodlný means comfortable. Its form changes according to gender:

• pohodlný = masculine singular
• pohodlná = feminine singular
• pohodlné = neuter singular

Since židle is feminine singular:

• židle je pohodlná = the chair is comfortable

So in the clause aby byla pohodlná, the adjective must also be feminine singular.

Yes. You may see both:

• je nastavená
• je nastavena

Both are correct, but they feel a bit different.

Very roughly:

• nastavená is the long adjectival form, common and natural in everyday speech
• nastavena is the short passive form, often sounding more formal, written, technical, or official

So:

• Je kancelářská židle nastavená tak, aby byla pohodlná?
  sounds normal and natural
• Je kancelářská židle nastavena tak, aby byla pohodlná?
  is also correct, but slightly more formal

Czech has no articles like English a/an/the.

So:

• kancelářská židle can mean
  an office chair, the office chair, or just office chair, depending on context.

In this sentence, English naturally uses the or the office chair, but Czech does not need to mark that directly.

If Czech wants to be more specific, it can use words like:

• ta kancelářská židle = that/the office chair

But in many situations, just kancelářská židle is enough.

Yes, Czech word order is fairly flexible, although not completely free.

The version given:

• Je kancelářská židle nastavená tak, aby byla pohodlná?

is a normal neutral question.

You might also hear variations depending on emphasis, for example:

• Je ta kancelářská židle nastavená tak, aby byla pohodlná?
  = Is that/the office chair adjusted so that it is comfortable?

Adding ta gives a stronger sense of referring to a specific chair.

But the basic pattern for a neutral yes/no question is very natural here:

• Je + subject + complement ... ?

In this sentence, tak is very natural because it pairs with aby and emphasizes the manner/result:

• nastavená tak, aby... = set in such a way that...

Sometimes Czech can omit tak, but with this kind of wording it usually sounds best to keep it.

Compare:

• Je židle nastavená tak, aby byla pohodlná?
  = very natural
• Je židle nastavená, aby byla pohodlná?
  possible in some contexts, but less standard/natural here

So for learners, tak, aby is a very useful pattern to remember.