In de diepvries is nog genoeg ruimte voor de rest van de soep.

Here de diepvries means the freezer.

In everyday Dutch, de diepvries and de vriezer can often both refer to the appliance where you keep frozen food. There can be slight nuance depending on region or context:

• de vriezer = the freezer appliance
• de diepvries = literally deep freeze, also commonly used for the freezer or frozen storage

So in this sentence, both would sound natural:

• In de diepvries is nog genoeg ruimte...
• In de vriezer is nog genoeg ruimte...

Because diepvries is a de-word in Dutch.

Dutch nouns take either:

• de
• het

Unfortunately, this is something you often have to learn together with the noun. So you learn:

• de diepvries
• de ruimte
• de rest
• de soep

Dutch often puts a place, time, or other adverbial phrase at the beginning of the sentence for emphasis or simply as a natural word-order choice.

The basic idea is:

• Er is nog genoeg ruimte in de diepvries...
• In de diepvries is nog genoeg ruimte...

When In de diepvries is moved to the front, the finite verb must come second. That is why you get:

• In de diepvries is nog genoeg ruimte...

This is a standard Dutch word-order rule: the conjugated verb usually stays in second position in main clauses.

The grammatical subject is genoeg ruimte.

So the structure is roughly:

• In de diepvries = in the freezer
• is = is
• nog genoeg ruimte = still enough space
• voor de rest van de soep = for the rest of the soup

Even though English often uses there is, Dutch does not need an equivalent here. The sentence is built around enough space is...

Here nog means still.

So nog genoeg ruimte means:

• still enough space
• enough space left

It suggests that space remains, even after something has already been put in or considered.

Compare:

• Er is genoeg ruimte. = There is enough space.
• Er is nog genoeg ruimte. = There is still enough space / There is enough space left.

Because ruimte here means space in a general, uncountable sense.

Just like in English, space is often uncountable:

• enough space not
• enough spaces

So:

• genoeg ruimte = enough space

If you were talking about different physical rooms or separate areas, then ruimtes could be plural, but not in this sentence.

Here voor means something like for or for storing.

The idea is:

• there is enough space for the rest of the soup

So ruimte voor iets is a very common Dutch pattern:

• ruimte voor de dozen = space for the boxes
• ruimte voor de auto = space for the car
• ruimte voor de rest van de soep = space for the rest of the soup

It means the rest of the soup or the remaining soup.

The pattern is:

• de rest van ... = the rest of ...

Examples:

• de rest van de dag = the rest of the day
• de rest van het eten = the rest of the food
• de rest van de soep = the rest of the soup

So it refers to the part of the soup that is left over.

Because Dutch often uses the definite article when talking about a specific thing already known in the context.

So:

• de soep = the soup

In this sentence, we are not talking about soup in general, but about a specific soup whose remainder needs to go into the freezer.

Yes, that would also be understandable.

For example:

• In de diepvries is nog genoeg ruimte voor de overgebleven soep.

That means There is still enough space in the freezer for the leftover soup.

But de rest van de soep is very natural and common, especially when you mean the part that remains of a particular soup.

Yes. A very useful pattern is:

• In/Op/Bij ... is nog genoeg ruimte voor ...

Examples:

• In de koelkast is nog genoeg ruimte voor het toetje.
  = There is still enough room in the fridge for the dessert.

• Op tafel is nog genoeg ruimte voor de borden.
  = There is still enough room on the table for the plates.

• In de kast is nog genoeg ruimte voor je jas.
  = There is still enough room in the cupboard for your coat.

So this sentence is a good model for talking about available space.