De nye er dyre, så jeg vil hellere beholde de gamle.

In Danish, adjectives can stand on their own when the noun is understood from context.

So de nye means something like the new ones and de gamle means the old ones.

The missing noun could be things like sko (shoes), biler (cars), stole (chairs), etc. Danish often leaves the noun out if it is obvious.

So:

• de nye = the new ones
• de gamle = the old ones

This works much like English the rich, the poor, or the old ones.

That -e ending is very common in Danish adjectives when they are:

• plural
• used after de
• or used in certain definite forms

In this sentence, de nye and de gamle are plural definite expressions, so the adjectives take -e.

Also, in er dyre, the adjective dyr becomes dyre because it describes something plural: de nye.

Compare:

• Den nye bil er dyr. = The new car is expensive.
• De nye biler er dyre. = The new cars are expensive.

So:

• singular: dyr
• plural: dyre

Here, de is not they.

In this sentence, de works like the in the new ones and the old ones.

Danish de can be confusing because it can mean different things depending on how it is used:

• de = they as a subject pronoun
• de = plural definite article, roughly the
• sometimes it can also feel close to those, depending on context

In de nye and de gamle, it is the article-like use: the new ones, the old ones.

Because the subject is plural.

The subject is de nye = the new ones, so the adjective after er must also be plural.

Danish predicate adjectives agree in number:

• Den er dyr. = It is expensive.
• De er dyre. = They are expensive.

So dyr is singular, while dyre is plural.

Hellere means rather.

So jeg vil hellere beholde de gamle means I would rather keep the old ones.

It is the comparative form connected to gerne:

• gerne = gladly / willingly / like to
• hellere = rather
• helst = preferably / most preferably

Examples:

• Jeg vil gerne blive. = I would like to stay.
• Jeg vil hellere blive. = I would rather stay.
• Jeg vil helst blive hjemme. = I would prefer most of all to stay home.

In Danish, with a modal verb like vil, adverbs such as hellere often come between the modal and the main infinitive.

So this pattern is very normal:

• jeg vil gerne spise
• jeg vil hellere vente
• jeg kan godt lide det

That is why jeg vil hellere beholde sounds natural.

You may sometimes see different word orders in special contexts, but for a learner, modal verb + adverb + infinitive is a very useful pattern.

Because it follows the modal verb vil.

After modal verbs in Danish, the next verb normally stays in the infinitive without at:

• jeg vil beholde
• jeg kan komme
• du må gå
• vi skal arbejde

So:

• vil = want to / will / would
• beholde = keep

Together, vil beholde means want to keep or, in this context, would rather keep.

Because så here is being used as a coordinating conjunction meaning so.

When så joins two main clauses like this, the second clause keeps normal main-clause word order:

• De nye er dyre, så jeg vil hellere beholde de gamle.

That is similar to English: The new ones are expensive, so I’d rather keep the old ones.

If the sentence began with an adverbial så meaning something like then, inversion could happen in other contexts. But here it is just linking two clauses, so jeg vil is normal.

Grammatically, yes. The expressions themselves do not tell you exactly what the missing noun is.

• de nye could mean the new ones, the new people, the new items, etc.
• de gamle could mean the old ones, the old people, the old items, etc.

The context decides.

In this sentence, because of dyre meaning expensive, the most likely meaning is objects or items, not people. People are not usually described as expensive in an ordinary literal sense.

Good question: dyr can mean two different things.

As an adjective:

• dyr = expensive

As a noun:

• et dyr = an animal

In this sentence, dyre is clearly the adjective form because it describes de nye.

Examples:

• Bilen er dyr. = The car is expensive.
• Hunden er et dyr. = The dog is an animal.

So the meaning depends on grammar and context.

Yes, that is a perfectly reasonable translation in many contexts.

More literally, jeg vil hellere beholde de gamle is I would rather keep the old ones.

But in natural English, I prefer to keep the old ones may also fit well.

The small difference is that would rather often sounds a bit more immediate or contrastive, especially after a reason:

• The new ones are expensive, so I’d rather keep the old ones.

That matches the Danish very well.