Hvis jeg havde mere tid senere på året, ville jeg besøge min ven.

Because havde here does not mainly show past time. It is part of a hypothetical / unreal condition.

Danish often uses the past tense in the if-clause to show that something is imagined rather than presented as a real fact:

• Hvis jeg har mere tid senere på året, besøger jeg min ven = if I do have more time later in the year, I visit / will visit my friend
• Hvis jeg havde mere tid senere på året, ville jeg besøge min ven = if I had more time later in the year, I would visit my friend

So havde marks the situation as less real, imagined, or contrary to the current situation.

Formally, yes: ville is historically the past tense of vil. But in sentences like this, it usually functions as would, not as a simple past wanted/will form.

Here:

• vil = will / want to
• ville = would

So ville jeg besøge min ven means I would visit my friend.

In a conditional sentence, ville is the normal choice for the result clause:

• Hvis ..., ville ...

In some contexts, ville can mean wanted to:

• Jeg ville hjem = I wanted to go home

But in this sentence, that is not the natural reading. Because it follows Hvis jeg havde..., the structure strongly signals a conditional meaning:

• Hvis ... , ville ... = If ... , would ...

So here ville is best understood as would, not wanted to.

Because after a modal verb like ville, Danish uses the infinitive.

So the pattern is:

• ville + infinitive
• kan + infinitive
• skal + infinitive
• må + infinitive

That is why you get:

• ville jeg besøge not
• ville jeg besøger

This is similar to English:

• I would visit not
• I would visits

This happens because Danish is a V2 language in main clauses. That means the finite verb usually comes in the second position.

In your sentence, the whole if-clause comes first:

• Hvis jeg havde mere tid senere på året

After that, the main clause begins. Since the first position is already occupied by the if-clause, the finite verb of the main clause comes next:

• ville jeg besøge min ven

So the structure is:

• first element: Hvis jeg havde mere tid senere på året
• second position: ville
• then subject: jeg

If the sentence started with the main clause instead, you would get normal-looking subject-verb order:

• Jeg ville besøge min ven, hvis jeg havde mere tid senere på året.

Because tid is an uncountable noun.

In Danish:

• mere = more, for uncountable things or amounts
• flere = more, for countable plural things

So:

• mere tid = more time
• flere bøger = more books

Since you cannot count time as separate items in this sentence, mere is correct.

It means later in the year.

Breakdown:

• senere = later
• på året = in the year / during the year

So the phrase places the imagined extra time at some point later in the same year.

A similar common expression is:

• senere i år = later this year

Both are natural, though senere på året sounds a bit more like later in the course of the year.

Because in Danish, a possessive like min normally replaces the article.

So:

• en ven = a friend
• vennen = the friend
• min ven = my friend

You do not combine min with en in this kind of phrase, and you do not use the definite ending -en after min here.

So min ven is the correct standard form.

Yes. You can also say:

• Jeg ville besøge min ven, hvis jeg havde mere tid senere på året.

This means the same thing.

The main difference is word order:

• When the sentence starts with the if-clause, the main clause becomes ville jeg ...
• When the sentence starts with the main clause, it stays jeg ville ...

Both are correct and natural.

Here you need hvis because this is a condition:

• Hvis jeg havde mere tid ... = If I had more time ...

Om is often used for whether / if in indirect questions, not for this type of conditional meaning:

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

So in your sentence, hvis is the right word.