Min veninde vil kun have et lille lån, hvis renten er lav.

Because veninde is a common-gender noun in Danish. Singular possessives agree with the noun’s gender:

• min for common gender
• mit for neuter
• mine for plural

So:

• min veninde
• mit lån
• mine venner

Veninde specifically means a female friend.
Ven usually means a male friend, though in some contexts it can also be used more generally for friend.

So min veninde tells you the speaker’s friend is female.

This is a very common Danish pattern: a modal verb + an infinitive.

• vil = wants to / will
• have = have, but here it can mean something like get or take in context

So vil have means wants to have / wants to get.

Also, after a modal verb like vil, Danish normally uses the infinitive without at:

• hun vil have
• not hun vil at have

Literally yes, but in context it often means take out, get, or want a loan.

So vil have et lille lån is not necessarily about already possessing a loan. It usually means she wants to obtain a small loan.

This is one of those cases where Danish uses have more naturally than English might.

Because kun is an adverb, and in a main clause Danish adverbs like this often come after the finite verb and before the infinitive or main verb material.

So:

• Min veninde vil kun have et lille lån

Here:

• vil = finite verb
• kun = adverb
• have = infinitive

This placement is very natural in Danish.

It also shows what kun is focusing on: she only wants a small loan, and only under that condition.

Because lån is a neuter noun, and neuter singular nouns take et in the indefinite form.

So:

• et lån
• et hus
• et problem

Compare common-gender nouns:

• en veninde
• en bil

You have to learn the gender of each noun, because it affects articles, possessives, and adjective agreement.

Because lille is irregular.

With many adjectives, a neuter singular noun would trigger -t:

• et stort hus
• et lavt niveau

But lille does not become lillet. It stays lille before singular nouns:

• en lille bil
• et lille lån

Its plural form is usually små:

• små lån

So this is something you mostly just memorize as a special pattern.

Renten is the definite form, meaning the interest rate.

Danish often adds definiteness directly to the noun with an ending:

• en rente = an interest rate
• renten = the interest rate

In this sentence, the speaker means a specific or contextually understood interest rate, so the definite form is natural.

Because lav here is a predicative adjective describing renten, and it agrees with the noun.

• renten is common gender singular
• so the adjective is lav

Compare:

• Renten er lav
• Niveauet er lavt

Here niveauet is neuter singular, so the adjective becomes lavt.

Because hvis introduces a subordinate clause.

In Danish, main clauses usually follow the V2 rule: the finite verb comes in second position. But subordinate clauses do not use that same word order. They usually keep the normal subject + verb order.

So:

• main clause: Renten er lav
• subordinate clause: hvis renten er lav

That is why you get hvis renten er lav, not something like hvis er renten lav.

Yes. If the subordinate clause comes first, the following main clause uses inversion, because Danish main clauses still follow the V2 rule.

Original order:

• Min veninde vil kun have et lille lån, hvis renten er lav.

With the hvis clause first:

• Hvis renten er lav, vil min veninde kun have et lille lån.

Notice that after the initial clause, the main clause begins with vil before min veninde.

Very often, yes. In this sentence it clearly means if in a conditional sense.

In some contexts, Danish hvis can also correspond to whether, but here the meaning is definitely conditional:

• if the interest rate is low

So in this sentence, you should understand hvis as if.