November er den måned, hvor jeg begynder at planlægge december mere præcist.

Because måned is a common-gender noun in Danish, not a neuter noun.

• en måned = a month
• den måned = that month / the month
• If it were a neuter noun, you would use det

In Danish, the gender of the noun decides whether you use den or det.

Both are possible in Danish, but November er den måned, hvor ... is especially natural when you are about to define or describe that month.

Here, den måned means something like:

• the month in which...
• the month when...

So the structure is setting up the following clause:

• November er den måned, hvor jeg begynder ...
• November is the month when I begin ...

Using den måned before the relative clause is very common.

Here hvor means when or in which, not literally just where.

In Danish, hvor is often used in relative clauses after words for time or place.

So:

• den måned, hvor jeg begynder ... means
• the month when I begin ...

Even though hvor often means where, in sentences like this it works like English when.

Normally, no. In modern Danish, hvor is the natural choice here.

• hvor is commonly used after nouns like dag, år, tid, måned, and so on in relative clauses.
• da is more often used as a conjunction meaning when in a specific past-time situation.

So in this sentence, hvor is the standard and idiomatic option.

Because begynde is commonly followed by at + infinitive.

So:

• jeg begynder at planlægge = I begin to plan

This is a very common Danish pattern:

• begynde at læse = begin to read
• begynde at arbejde = begin to work
• begynde at tænke = begin to think

So at here works like English to before an infinitive.

Because month names in Danish are normally used without an article, just like in English.

• i november = in November
• december = December

So at planlægge december simply means to plan December.

This sounds natural if you mean planning the month as a whole: schedules, events, holidays, tasks, and so on.

Mere præcist means more precisely, more specifically, or in more detail.

• præcist = precisely
• mere præcist = more precisely

So the idea is:

• in November, I start planning December
• and I do it in a more exact or detailed way

It modifies planlægge, so it describes how the planning is done.

Because here the word is being used adverbially, not as an adjective describing a noun.

Compare:

• en præcis plan = a precise plan
  
  • here præcis is an adjective
• at planlægge præcist = to plan precisely
  
  • here præcist is used like an adverb

In Danish, many adjectives take -t when used adverbially.

So:

• præcis = adjective form
• præcist = adverb-like form

And then:

• mere præcist = more precisely

Because hvor jeg begynder at planlægge december mere præcist is a subordinate clause, not a main clause.

In Danish:

• main clauses usually follow V2 word order: the finite verb comes early
• subordinate clauses usually have subject before the finite verb

So:

• Main clause: Jeg begynder at planlægge december.
• Subordinate clause: ..., hvor jeg begynder at planlægge december.

That is why jeg comes before begynder here.

Yes. Danish often uses the present tense for things that are generally true, habitual, or repeated regularly.

So:

• November er den måned, hvor jeg begynder ... means something like
• November is the month when I start ... or
• November is the month in which I usually start ...

It does not have to mean only this exact year. It can describe a regular personal pattern.

Yes, it is understandable and natural, especially if you mean organizing the month as a whole.

It suggests things like:

• planning appointments
• planning holiday events
• planning travel
• planning family activities
• planning work or deadlines in December

So planlægge december means something broader than planning one single event. It means planning what December will look like.

You could say:

• November var den måned, hvor jeg begyndte at planlægge december mere præcist.

Changes:

• er → var
• begynder → begyndte

That means:

• November was the month when I began planning December more precisely.

So the structure stays the same; only the tense changes.