De klimmer zou liever rusten dan dat hij de klimroute afmaakt.

Zou is the conditional form of zullen. In this sentence, it makes the meaning closer to English would rather.

• De klimmer rust liever ... = The climber prefers to rest ... / The climber would rather rest ... in a more direct, present statement
• De klimmer zou liever rusten ... = The climber would rather rest ... with a more conditional, less direct, or more hypothetical feel

So zou does not mean future here. It helps create the idea of would rather.

Dutch uses liever when talking about preference between options.

• graag = gladly / with pleasure / like doing
• liever = rather / prefer

Compare:

• Ik rust graag. = I like resting.
• Ik rust liever. = I’d rather rest.

In your sentence, the climber is being presented with two alternatives:

• resting
• finishing the climbing route

Because it is a comparison of preference, Dutch uses liever.

After zou, Dutch normally uses an infinitive at the end of that verbal group. Here, that infinitive is rusten.

So the first part is:

• De klimmer zou liever rusten
  literally: The climber would rather rest

This is a very common pattern:

• Ik zou liever thuisblijven. = I would rather stay home.
• Zij zou liever wachten. = She would rather wait.

Because the second part is a full clause with its own subject and finite verb:

• hij = subject
• afmaakt = finite verb

Dutch often uses:

• dan
  • word/phrase
• dan dat
  • full clause

So:

• Ik drink liever thee dan koffie.
  = I’d rather drink tea than coffee.
• Ik drink liever thee dan dat ik koffie drink.
  = I’d rather drink tea than drink coffee.

In your sentence, the second part is a clause:

• dan dat hij de klimroute afmaakt

That is why dat appears.

Yes, Dutch speakers often use simpler alternatives, especially when the subject is the same.

For example:

• De klimmer zou liever rusten dan de klimroute afmaken.

This is very natural and probably the more straightforward version for many learners. It avoids repeating hij.

The version with dan dat hij ... afmaakt is also correct, but it sounds more explicitly contrastive and a bit more formal or careful in structure.

It may be obvious in meaning, but once Dutch uses a full clause after dan dat, that clause normally needs its own subject.

So:

• dan dat hij de klimroute afmaakt

works like:

• than that he finishes the climbing route

Even though English usually avoids saying it that way, Dutch clause structure makes the repeated subject normal here.

If you want to avoid repeating the subject, Dutch often switches to the shorter infinitive construction:

• De klimmer zou liever rusten dan de klimroute afmaken.

Because dan dat introduces a subordinate clause, and in Dutch subordinate clauses the finite verb usually goes to the end.

Main clause:

• De klimmer zou liever rusten
• word order is more like normal main-clause order

Subordinate clause:

• dat hij de klimroute afmaakt
• the finite verb afmaakt comes at the end

This is a very important Dutch pattern:

• Ik weet dat hij komt. = I know that he is coming.
• Omdat zij moe is, rust zij. = Because she is tired, she rests.

So afmaakt is at the end because it belongs to a subordinate clause.

The verb is afmaken, which is a separable verb.

In a main clause, separable verbs split:

• Hij maakt de klimroute af.

But in subordinate clauses, the two parts stay together at the end:

• ... dat hij de klimroute afmaakt

So this sentence is following the normal rule for separable verbs in subordinate clauses.

Compare:

• Zij belt haar moeder op.

• ... omdat zij haar moeder opbelt

• Hij maakt het werk af.
• ... dat hij het werk afmaakt

No. Afmaken does not simply mean make here. It means something like:

• finish
• complete
• see through to the end

So:

• de klimroute afmaken = finish the climbing route

That is a common meaning of afmaken when talking about tasks, work, or something that can be completed.

Dutch often uses the definite article when talking about a specific thing already understood in the situation.

So de klimroute means:

• the climbing route

It suggests a particular route, not just any route.

If you said een klimroute, that would mean:

• a climbing route

which would sound less specific.

It is correct Dutch, but many speakers would probably choose a slightly simpler version in everyday speech:

• De klimmer zou liever rusten dan de klimroute afmaken.

That version is shorter and avoids the full dan dat clause.

The original sentence is still useful for learners because it clearly shows:

• zou liever for would rather
• dan dat introducing a full clause
• subordinate clause word order
• separable verb behavior in a subordinate clause

So it is grammatical and meaningful, even if a simpler alternative may be more common in ordinary conversation.

A useful way to see it is:

• Subject + zou + liever + infinitive + dan dat + subject + object + finite verb

Applied to your sentence:

• De klimmer = subject
• zou = conditional helper
• liever = rather
• rusten = infinitive
• dan dat = than that / rather than
• hij = subject of the second clause
• de klimroute = object
• afmaakt = finite verb at the end

So the whole sentence is built as a comparison between two actions:

1. resting
2. finishing the route

with the meaning that the first action is preferred over the second.