Služebna je dnes otevřená.

Služebna is a feminine noun. Its exact English translation depends on context.

Common possibilities include:

• station
• office
• duty office / duty room
• in many contexts, especially police-related, police station

So Služebna je dnes otevřená. can mean something like The station/office is open today.

Je means is.

The sentence structure is:

• Služebna = the station/office
• je = is
• dnes = today
• otevřená = open

So the grammar is very similar to English:
The station is open today.

Unlike in some other Slavic languages, Czech normally does use the verb být (to be) in the present tense:

• Služebna je otevřená. = The station is open.

Because otevřená is an adjective, and it agrees with služebna.

Služebna is:

• feminine
• singular
• nominative

So the adjective must also be feminine singular nominative:

• masculine: otevřený
• feminine: otevřená
• neuter: otevřené

Examples:

• Obchod je otevřený. = The shop is open.
• Služebna je otevřená. = The station is open.
• Muzeum je otevřené. = The museum is open.

That is a very common question.

On signs, Czech often uses:

• Otevřeno = Open
• Zavřeno = Closed

This is a fixed, very common public sign style.

But when you describe a specific noun, the adjective usually agrees with that noun:

• Služebna je otevřená.
• Obchod je otevřený.
• Kancelář je otevřená.

So:

• otevřeno = a general sign-style expression, Open
• otevřená = adjective agreeing with služebna

Both relate to the same idea, but they are used differently.

Yes. Otevřena is also possible.

There is a difference in style:

• otevřená sounds like the normal everyday adjectival form
• otevřena is a shorter form that often sounds more formal, official, or written

So:

• Služebna je dnes otevřená. = natural everyday Czech
• Služebna je dnes otevřena. = more formal/official style

A learner will hear both, but otevřená is very safe and natural in ordinary speech.

Yes, Czech word order is flexible.

Služebna je dnes otevřená. is a very normal neutral sentence.

You can also change the order:

• Dnes je služebna otevřená.
• Služebna je otevřená dnes.

But the emphasis changes:

• Služebna je dnes otevřená.
  Neutral: the station is open today.

• Dnes je služebna otevřená.
  Emphasis on today.

• Služebna je otevřená dnes.
  Often sounds contrastive, like today (not some other day).

So the original sentence is a natural, neutral choice.

It is in the nominative singular.

That is because služebna is the subject of the sentence:

• Služebna je dnes otevřená.
  The station is open today.

The subject of a sentence is normally in the nominative.

Because Czech does not have articles like English a/an/the.

So služebna can mean:

• a station
• the station

Context tells you which one is meant.

In a sentence like this, English will often use the:

• The station is open today.

But Czech simply says:

• Služebna je dnes otevřená.

A rough pronunciation guide is:

• služebna ≈ SLOO-zheb-na
• stress is on the first syllable: SLU-žeb-na

A few details:

• ž sounds like the s in measure
• Czech stress is usually on the first syllable
• the final a is pronounced clearly, not reduced away

So the most important thing is:

• first-syllable stress
• ž = zh sound

In this sentence, it is best understood as an adjective meaning open.

So the pattern is:

• noun + je
  • adjective

That is why it agrees with služebna:

• služebna → feminine
• otevřená → feminine

In practice, for a learner, the easiest way to read this sentence is simply:

• Služebna = subject
• je = is
• otevřená = open

So: The station is open today.