Jo længere jeg læser bogen, jo bedre forstår jeg teksten.

It is a very common Danish pattern that matches the English the ... the ... comparative structure.

So:

• Jo længere jeg læser bogen ... = The longer I read the book ...
• ... jo bedre forstår jeg teksten = ... the better I understand the text

In this pattern, jo does not have a separate literal meaning like yes or indeed. It is just part of the fixed comparative structure.

Because længere is the comparative form, meaning longer.

Here is the basic idea:

• lang = long (adjective)
• længe = for a long time / long (adverb)
• længere = longer

In this sentence, it describes the duration of the reading, so it works adverbially: the longer I read.

After jo in this construction, Danish normally uses a comparative form, so længere is exactly what you expect.

Bedre is the comparative form of god/godt, and it is irregular, just like English good → better.

So:

• god = good
• godt = well / good in some uses
• bedre = better

In this sentence, bedre means better in the sense of more successfully / more clearly understanding the text.

This is a very useful Danish word-order point.

In the second clause, jo bedre comes first. Danish main clauses follow the verb-second rule, so when something other than the subject is placed first, the finite verb must come next:

• jo bedre = first position
• forstår = finite verb in second position
• jeg = subject after the verb

That is why you get:

• jo bedre forstår jeg teksten

and not:

• jo bedre jeg forstår teksten

In the first jo clause, Danish normally keeps the order subject + verb:

• jo længere jeg læser bogen

So the two halves do not look identical, even though they belong to the same overall pattern.

Danish does not have a separate everyday progressive tense like English am reading.

So the simple present læser can cover meanings like:

• read
• am reading
• do read, depending on context

Here, jeg læser bogen naturally means something like I am reading the book or as I keep reading the book.

Because Danish usually makes nouns definite by adding the definite article to the end of the noun.

So:

• bog = book
• bogen = the book
• tekst = text
• teksten = the text

This is completely normal Danish grammar.

A separate word like den is usually used when there is an adjective:

• bogen = the book
• den interessante bog = the interesting book

Yes. In standard written Danish, the comma separates the two clauses:

• Jo længere jeg læser bogen, jo bedre forstår jeg teksten.

It helps show the two linked parts of the comparison clearly. In this kind of sentence, the comma is normal and expected.

It is the same form, jo, but it has a different function here.

Danish jo can do several jobs depending on context. For example, it can be used:

• as a reply meaning something like yes, actually
• as a particle meaning something like after all / as you know
• as part of this fixed comparative pattern jo ... jo ...

So in this sentence, you should treat it as part of the special structure, not as the everyday reply word jo.

Yes, very often. It is a productive pattern in Danish.

For example:

• Jo mere du øver dig, jo bedre bliver du.
  The more you practise, the better you become.

• Jo tidligere vi starter, jo hurtigere bliver vi færdige.
  The earlier we start, the faster we finish.

• Jo mindre han siger, jo mere mystisk virker han.
  The less he says, the more mysterious he seems.

So once you learn the pattern, you can use it with many comparatives.

There is no special grammar rule behind that choice. It is mostly about meaning and style.

The sentence suggests:

• you are reading the book
• and as you continue, you understand the text better

Since a book contains text, this is perfectly natural. Using teksten in the second half can sound slightly more precise, because it focuses on the actual written content rather than the physical book.

You could sometimes repeat bogen, but teksten makes good sense here.