Hvis jeg havde flere penge, ville jeg købe flere bøger.

Because this sentence is a hypothetical or unreal condition. Danish often uses the past form in the hvis-clause to talk about something that is not true now, or is only imagined:

• Hvis jeg har flere penge ... = if I have more money ...
• Hvis jeg havde flere penge ... = if I had more money ...

So havde here works very much like English had in If I had more money...

For the same reason: the sentence is hypothetical.

• vil usually means will
• ville here means would

So:

• Jeg vil købe flere bøger = I will buy more books
• Jeg ville købe flere bøger = I would buy more books

In this kind of sentence, Danish normally uses havde ... ville ... for a present/future unreal situation.

Yes, that is the normal implication.

Hvis jeg havde flere penge, ville jeg købe flere bøger strongly suggests that the speaker does not currently have as much money as they would like. That is why it is called an unreal or counterfactual condition.

It does not absolutely prove the facts in every context, but in normal use, that is what listeners will understand.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

Here, the whole Hvis jeg havde flere penge clause comes first. After that, the main clause begins, and the finite verb ville must come before the subject jeg:

• Hvis jeg havde flere penge, ville jeg købe flere bøger.

If you put the main clause first, the word order is normal again:

• Jeg ville købe flere bøger, hvis jeg havde flere penge.

So the inversion happens because the hvis-clause is placed first.

Because ville is a modal verb, and after modal verbs Danish uses the bare infinitive.

So you get:

• ville købe
• kan købe
• skal købe
• må købe

not:

• ville at købe

This is similar to English would buy, not would to buy.

Normally, no. In this sentence you need hvis.

Hvis is used for a real or imagined condition:

• Hvis jeg havde flere penge ... = if I had more money ...

Om is more often used for whether / if in the sense of uncertainty:

• Jeg ved ikke, om han kommer = I don't know whether he is coming

So in conditional sentences like this one, hvis is the normal choice.

Because Danish penge is grammatically a plural-only noun. Even though English says money, Danish uses penge, which behaves like a plural noun.

That is why Danish says:

• flere penge = more money

not:

• mere penge

A useful comparison is:

• flere penge = more money
• mere tid = more time

So flere is used with plural/count-style nouns, while mere is used with non-count nouns like tid, vand, or arbejde.

Because bøger is a plural count noun: books.

So:

• en bog = a book
• bøger = books
• flere bøger = more books

This is exactly what you would expect with a normal plural noun. The interesting part is really penge, because Danish treats that as plural too.

Because Danish, like English, often uses no article with an indefinite plural noun.

• flere bøger = more books
• mange bøger = many books
• nogle bøger = some books

You do not need an article like en/et there, because those are singular. And Danish does not add a separate plural indefinite article in this kind of phrase.

Yes, but it changes the meaning slightly.

• ville jeg købe = I would buy
  This focuses on what I would choose or intend to do.
• kunne jeg købe = I could buy / I would be able to buy
  This focuses on possibility or ability.

So both are grammatical, but they are not exactly the same:

• Hvis jeg havde flere penge, ville jeg købe flere bøger = If I had more money, I would buy more books.
• Hvis jeg havde flere penge, kunne jeg købe flere bøger = If I had more money, I could buy more books.

Because the sentence begins with a subordinate hvis-clause, followed by the main clause:

• Hvis jeg havde flere penge, = subordinate clause
• ville jeg købe flere bøger = main clause

The comma marks the boundary between the two clauses. In written Danish, this is standard.

Yes. This is a very natural and standard way to say it.

The pattern is:

• Hvis + past form ..., ville + infinitive

For example:

• Hvis jeg havde mere tid, ville jeg læse mere.
• Hvis hun boede tættere på, ville hun komme oftere.

So your sentence is a textbook example of a Danish hypothetical conditional.