Jo mindre kaffe jeg drikker om aftenen, jo bedre sover jeg.

It is the Danish equivalent of English the ..., the ... in sentences like:

• The less coffee I drink, the better I sleep.
• The more you practice, the better you get.

So jo mindre ..., jo bedre ... expresses a relationship between two changes:

• if one thing goes down, another changes
• if one thing goes up, another changes

In this sentence:

• jo mindre kaffe jeg drikker om aftenen = the less coffee I drink in the evening
• jo bedre sover jeg = the better I sleep

Because kaffe is an uncountable noun, like coffee in English.

In Danish:

• mindre = less, for uncountable amounts
• færre = fewer, for countable things

So:

• mindre kaffe = less coffee
• færre kopper kaffe = fewer cups of coffee

A native English speaker may notice this works just like the English less vs fewer distinction.

Because kaffe is being used as a mass noun in a general sense.

Danish, like English, often uses mass nouns without an article when talking about the substance in general:

• Jeg drikker kaffe. = I drink coffee.
• Jeg drikker mindre kaffe. = I drink less coffee.

You would only add an article if you meant a specific coffee in a specific context, which is not the case here.

This is a very good word-order question.

In jo ... jo ... sentences, the two parts behave differently:

1. The first jo clause often has subordinate-clause word order:

   • jo mindre kaffe jeg drikker om aftenen
   • subject jeg comes before the finite verb drikker

2. The second jo clause behaves like a main clause with the comparative phrase in first position:

   • jo bedre sover jeg
   • the fronted element jo bedre takes first position, so the verb sover comes before the subject jeg because of normal Danish V2 word order

So the difference is grammatical, not random.

Because bedre is the comparative form of god/godt.

Compare:

• god = good
• godt = well / good (neuter or adverbial form in some contexts)
• bedre = better

Here the sentence means I sleep better, so Danish uses bedre:

• Jeg sover godt. = I sleep well.
• Jeg sover bedre. = I sleep better.

So bedre is exactly what you need because the sentence is making a comparison.

Om aftenen means in the evening or in the evenings in a general, habitual sense.

That fits this sentence because it is talking about a repeated pattern or habit, not one specific evening.

Compare:

• om aftenen = in the evening / in the evenings, generally
• i aften = tonight
• om morgenen = in the morning
• om natten = at night

So:

• Jeg drikker kaffe om aftenen. = I drink coffee in the evening / in the evenings.
• Jeg drikker kaffe i aften. = I’m drinking coffee tonight.

Because it expresses a general truth or habitual relationship.

Danish often uses the present tense for things that are regularly true:

• Jo mindre kaffe jeg drikker om aftenen, jo bedre sover jeg.

This does not mean only right now. It means something like:

• whenever this happens, this is the result
• as a general rule, less evening coffee leads to better sleep

English does the same:

• The less coffee I drink in the evening, the better I sleep.

No. Jo has several uses in Danish.

In this sentence, jo is part of the fixed comparative pattern jo ..., jo ... = the ..., the ....

But elsewhere jo can also be a reply particle, often meaning something like yes, actually when contradicting a negative statement:

• Du kommer ikke.
• Jo, det gør jeg.
• You’re not coming.
• Yes, I am.

So the jo in your sentence is not that kind of jo. Here it is purely part of the comparison structure.

Yes. It is a full clause, even though it begins with the comparative phrase.

Its parts are:

• jo mindre kaffe = the less coffee
• jeg = I
• drikker = drink
• om aftenen = in the evening

So the underlying clause is:

• jeg drikker mindre kaffe om aftenen = I drink less coffee in the evening

The jo makes it part of the larger the ..., the ... pattern.

Yes, that is possible, but it is not exactly the same nuance.

• Hvis jeg drikker mindre kaffe om aftenen, sover jeg bedre = If I drink less coffee in the evening, I sleep better.
• Jo mindre kaffe jeg drikker om aftenen, jo bedre sover jeg = The less coffee I drink in the evening, the better I sleep.

The hvis version sounds more like a condition. The jo ..., jo ... version emphasizes a sliding relationship: as one amount decreases, the other improves.

So both are natural, but the original sentence expresses the comparison more precisely.

Not very naturally.

A rough word-for-word mapping is:

• Jo = the
• mindre = less
• kaffe = coffee
• jeg = I
• drikker = drink
• om aftenen = in the evening
• jo = the
• bedre = better
• sover = sleep
• jeg = I

But if you follow Danish word order too closely, the English will sound wrong. The natural English structure is:

• The less coffee I drink in the evening, the better I sleep.

So it is better to learn jo ..., jo ... as a whole pattern rather than trying to translate each word mechanically.