De winkel is nog open.

Because winkel is a de-word. In Dutch, singular nouns take either de or het as their definite article, and winkel belongs to the de group.

So:

• de winkel = the shop/store
• de winkels = the shops/stores

There is not always a simple rule you can rely on, so it is best to learn nouns together with their article.

Here nog means still.

So the sentence means that the shop/store is still open.

Be careful, though: nog can mean different things in different contexts, such as still, yet, another, or more. In this sentence, the natural meaning is still.

Dutch main clauses normally follow the verb-second rule. That means the finite verb comes in the second position of the sentence.

Here the order is:

• De winkel = subject
• is = finite verb
• nog open = rest of the sentence

So:

• De winkel is nog open.

You can see the same rule if another element comes first:

• Vandaag is de winkel nog open.

The verb is still stays in second position.

Yes. Open is an adjective here, describing the state of the shop.

Dutch often uses an adjective after zijn:

• De deur is open.
• Het raam is dicht.
• De winkel is open.

Also note that after zijn, the adjective does not get an extra -e ending. So it stays open, not opene.

Yes, but geopend is usually more formal or official-sounding.

In everyday Dutch, open is much more common for shops, doors, restaurants, and so on:

• De winkel is open.

You might see geopend on signs, notices, or in more formal language, but for normal conversation, open is the safer and more natural choice.

The most common negative version is:

• De winkel is nog niet open.

That usually means The shop is not open yet.

A very useful pattern is:

• nog niet = not yet

So:

• De winkel is nog open. = The shop is still open.
• De winkel is nog niet open. = The shop is not open yet.

Normally, no. In standard Dutch, a singular countable noun usually needs an article in a sentence like this.

So the normal form is:

• De winkel is nog open.

Without de, it sounds incomplete or unnatural, except in special cases like headlines, labels, or very telegraphic notes.

It can match either shop or store, depending on the variety of English.

• In British English, shop is often the closest match.
• In American English, store is often the most natural translation.

So winkel is a general word for a place where things are sold.

A rough pronunciation guide is:

• de ≈ duh
• winkel ≈ VING-kul
• is ≈ iss
• nog has a short o and a guttural Dutch g
• open ≈ OH-puhn

Very roughly:

• duh VING-kul iss nogh OH-puhn

For many English speakers, the hardest sound here is the g in nog, because Dutch g is usually much harsher than English g.