Książkomat jest przed biblioteką.

Książkomat is a modern compound noun. It is built from książka (book) plus -mat, a part used in names of automated machines or lockers, as in paczkomat.

So książkomat means something like book machine, usually an automated locker or self-service pickup/return machine for library books.

Grammatically, it behaves like a normal singular noun.

Because after przed in this sentence, Polish uses the instrumental case.

The basic dictionary form is biblioteka.
But in przed biblioteką (in front of the library), the noun changes form:

• biblioteka → nominative
• biblioteką → instrumental singular

This is very common with feminine nouns ending in -a:

• szkoła → szkołą
• ulica → ulicą
• biblioteka → biblioteką

Because przed means a location here: in front of.

When Polish expresses a static position with przed, it normally uses the instrumental:

• przed biblioteką = in front of the library
• przed domem = in front of the house
• przed szkołą = in front of the school

So the sentence is describing where the book locker is, not movement.

Not always.

• For location: usually instrumental

  • Jest przed biblioteką. = It is in front of the library.

• For movement to a position in front of something: often accusative

  • Wyjdź przed bibliotekę. = Go out in front of the library.

So the case depends on whether you mean being somewhere or moving to somewhere.

In a normal sentence like this, jest is expected.

Jest is the 3rd person singular of być (to be), and it is used in ordinary location sentences:

• Książkomat jest przed biblioteką.

If you leave it out, the result sounds incomplete, headline-like, or very elliptical:

• Książkomat przed biblioteką.

That might appear on a sign or in very informal shorthand, but it is not the neutral full sentence.

Książkomat is:

• nominative singular in this sentence, because it is the subject
• masculine inanimate, because it names a thing and ends in a consonant

So the structure is:

• Książkomat = subject
• jest = verb
• przed biblioteką = prepositional phrase showing location

No, it is not a proper noun here. It is capitalized simply because it is the first word of the sentence.

If it appeared in the middle of a sentence, it would normally be lowercase:

• Przed biblioteką jest książkomat.

Yes. Polish word order is fairly flexible.

The version you have is neutral and straightforward:

• Książkomat jest przed biblioteką.

You could also say:

• Przed biblioteką jest książkomat.

That version puts more focus on the location. It can sound natural if you are answering a question like Where is the book locker?

So the meaning stays basically the same, but the emphasis changes.

Because Polish does not use articles like a, an, and the.

So książkomat can mean:

• a book locker
• the book locker

The exact meaning depends on context.

In this sentence, English often uses the because the location suggests a specific one:
The book locker is in front of the library.

A few helpful points:

• Polish stress is usually on the second-to-last syllable
• książkomat is stressed as książKOmat
• biblioteką is stressed as biblioTEką

Also:

• ą is a nasal vowel
• in książkomat, the ą is before a consonant, so it sounds roughly like a nasal o
• in biblioteką, final ą is also nasal, though in everyday speech it may sound a bit lighter than learners expect

If pronunciation feels difficult, the hardest parts are usually:

• the cluster książ-
• the nasal vowel ą

Its core meaning is in front of the library.

In real life, speakers may use it a bit loosely if something is clearly located just outside the building, but the literal spatial meaning is specifically in front of, not just near or outside in a general sense.

So if you want the most accurate translation, in front of the library is the best one.