Казино открыто всю ночь.

Russian usually omits the present-tense form of to be.

So:

• Казино открыто = The casino is open
• Literally, it looks like Casino open

This is completely normal in Russian.
If you wanted past or future, then a form of быть would appear:

• Казино было открыто = The casino was open
• Казино будет открыто = The casino will be open

Открыто here is the short form of the adjective открытый (open).

Russian often uses the short form of adjectives after a noun to describe its state or condition, especially in sentences like:

• Дверь открыта = The door is open
• Магазин закрыт = The store is closed
• Казино открыто = The casino is open

So:

• открытый = full form, more like open as a descriptive adjective
• открыто = short form, used predicatively, meaning is open

This is one of the most common patterns learners see with words like открыт / открыта / открыто / открыты and закрыт / закрыта / закрыто / закрыты.

Because казино is treated as a neuter noun in Russian.

Even though казино ends in -о and is borrowed from another language, in Russian it is an indeclinable neuter noun. That means the adjective has to agree with it in gender and number:

• masculine: магазин открыт
• feminine: дверь открыта
• neuter: казино открыто
• plural: магазины открыты

So открыто matches the noun казино.

No. Казино is one of many indeclinable borrowed nouns in Russian.

That means it usually stays the same in all cases:

• Я вижу казино = I see the casino
• У казино = by the casino
• В казино = in the casino

Even though the noun does not change, other words around it can still show its role in the sentence.

Всю ночь is in the accusative case.

The expression means all night and is used as an adverbial phrase of duration. In Russian, expressions showing how long something lasts often use the accusative:

• весь день = all day
• всю неделю = all week
• всю ночь = all night

Here the base noun is:

• ночь = night (feminine)

Its accusative singular form is:

• ночь → ночь
  and the adjective changes:

• вся → всю

So:

• всю ночь = the whole night / all night

Because ночь is an inanimate feminine noun, and its accusative singular form happens to look the same as the nominative singular.

So:

• nominative: ночь
• accusative: ночь

But the adjective still clearly shows the case:

• nominative feminine: вся ночь
• accusative feminine: всю ночь

This is very common in Russian: sometimes the noun form stays the same, but the adjective makes the case obvious.

You might hear expressions like that in some contexts, but всю ночь is the most natural and standard way to say all night here.

Compare:

• всю ночь = all night, the whole night
• целую ночь = the whole night / an entire night

Both can be understandable, but for a general statement about opening hours, Казино открыто всю ночь is the most idiomatic choice.

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

The neutral order here is:

• Казино открыто всю ночь.

This sounds like a simple statement of fact.

You could also change the order for emphasis, for example:

• Всю ночь казино открыто.
  This puts more emphasis on all night.

But if you are just learning, the original order is the best one to use.

In practical learner terms, it is best understood here as the short form of the adjective открытый.

Historically and grammatically, forms like открыт / открыта / открыто / открыты are closely connected with participial/adjectival formation, and you may see grammar books discuss that in more detail. But for this sentence, the important point is simple:

• Казино открыто means The casino is open
• It describes a state
• It agrees with the noun in gender/number

So for everyday learning, think of it as the normal Russian way to say something is open.

A simple pronunciation guide is:

• Казино → ka-zee-NO
• открыто → at-KRY-ta
• всю ночь → fsyu NOCH

A more careful approximation of the whole sentence:

• ka-zee-NO at-KRY-ta fsyu NOCH

A few helpful notes:

• Stress falls on -но in казино
• Stress falls on -кры- in открыто
• всю begins with a sound close to fsyu, because в before с is devoiced
• ч in ночь sounds like ch in chat, but softer

Yes. In normal usage, those ideas are basically the same here.

Казино открыто всю ночь means the casino remains open throughout the night. In English, depending on context, you might translate it as:

• The casino is open all night.
• The casino stays open all night.
• The casino is open the whole night.

The Russian sentence itself is a straightforward statement about duration of being open.