Biblioteka jest czynna od ósmej do dziesiątej.

Czynna means open in the sense of open for business / operating.

In Polish, places such as shops, libraries, offices, and museums are often described as:

• czynny / czynna / czynne = open
• nieczynny / nieczynna / nieczynne = closed, not operating

So Biblioteka jest czynna means that the library is open and functioning at that time.

Because czynna has to agree with biblioteka.

Biblioteka is a feminine noun, so the adjective also takes the feminine singular form:

• czynny — masculine
• czynna — feminine
• czynne — neuter / plural in some contexts

Since biblioteka is feminine, Polish uses czynna.

Because the prepositions od and do require the genitive case.

So the time expressions change form:

• ósma → ósmej
• dziesiąta → dziesiątej

This is very common in Polish:

• od pierwszej do trzeciej
• od piątej do szóstej
• od ósmej do dziesiątej

So after od and do, you should expect these case forms.

Because Polish tells the hour using an implied feminine noun: godzina.

So o ósmej literally means something like at the eighth hour, where godzina is understood but not spoken.

That is why the forms are feminine:

• ósma godzina → o ósmej
• dziesiąta godzina → do dziesiątej

Even when godzina is not said, it still controls the grammar.

Yes, very often.

You can say:

• Biblioteka jest czynna od ósmej do dziesiątej.
• Biblioteka czynna od ósmej do dziesiątej.

The version without jest is very common on signs, notices, schedules, and official information.
The version with jest sounds like a full neutral sentence in normal speech.

Yes. Biblioteka jest otwarta od ósmej do dziesiątej is also natural.

There is a slight difference in feel:

• czynna = open, operating, available for service
• otwarta = open

For places like libraries, shops, offices, and institutions, both can work, but czynna is especially common in formal or practical information such as opening hours.

Not by itself. It simply means from eight to ten.

Whether that is morning or evening depends on context. In everyday situations, many people would assume morning unless something suggests otherwise, but the sentence itself does not explicitly say AM or PM.

If you want to make it clear, you can add words like:

• rano = in the morning
• wieczorem = in the evening

For example:

• Biblioteka jest czynna od ósmej rano do dziesiątej wieczorem.

Biblioteka jest czynna od ósmej do dziesiątej is the most neutral, straightforward order.

Polish word order is more flexible than English, so other orders are possible, for example to emphasize the time:

• Od ósmej do dziesiątej biblioteka jest czynna.

But the original order is the most natural if you are simply stating the opening hours.

A rough pronunciation guide is:

• ósmej ≈ OOS-mey
• dziesiątej ≈ jye-SYON-tey

A few useful points:

• ó is pronounced like u
• dz in dziesiątej is part of one sound cluster
• ą before t is often pronounced somewhat like on

So dziesiątej sounds roughly like jye-SYON-tey, not like the English word ten.

A few common opposites are:

• Biblioteka jest nieczynna. = The library is closed / not open.
• Biblioteka jest zamknięta. = The library is closed.

Both are common, but:

• nieczynna often appears in practical/public information
• zamknięta is the more direct everyday word for closed

So on a sign, nieczynna is especially likely.