Wer aussetzt, darf eine Karte nachziehen.

Here wer does not mean just who? as a question word. It means whoever or anyone who.

So:

• Wer aussetzt, ... = Whoever skips a turn, ...
• Wer aussetzt, darf ... = Anyone who skips a turn may/is allowed to ...

This use of wer is very common in German.

Because Wer aussetzt is a subordinate clause (more specifically, a clause introduced by wer), and in German subordinate clauses the finite verb goes to the end.

So the order is:

• Wer = whoever
• aussetzt = skips/sits out

Compare:

• Er setzt aus. = He skips a turn.
• Wer aussetzt, ... = Whoever skips a turn, ...

In the second sentence, the verb moves to the end because of the clause structure.

Yes. Aussetzen is a separable verb.

In a normal main clause, it splits:

• Er setzt aus.

But in places where German keeps the verb together—such as:

• subordinate clauses
• infinitives
• past participles

it stays as one word:

• ..., weil er aussetzt.
• aussetzen
• ausgesetzt

So aussetzt is exactly what you would expect in this clause.

In this context, aussetzen means something like:

• to skip a turn
• to sit out a round
• to miss a go

The exact English wording depends on the game, but it usually means the player does not take a normal turn at that moment.

Because the sentence begins with a subordinate clause:

• Wer aussetzt, = Whoever skips a turn,
• darf eine Karte nachziehen. = may draw an extra card.

German uses a comma to separate this introductory clause from the main clause.

Darf is from dürfen, which usually expresses permission.

So here it means:

• may
• is allowed to

It does not mean must.

So:

• Wer aussetzt, darf eine Karte nachziehen.
• = Whoever skips a turn may draw another card.

Depending on context, English might also use gets to.

Because nachziehen depends on the modal verb darf.

With a modal verb in German, the second verb goes to the end in the infinitive:

• Er darf eine Karte nachziehen.

Since nachziehen is a separable verb, it stays unsplit in the infinitive.

Compare:

• Er zieht eine Karte nach. = He draws an extra card.
• Er darf eine Karte nachziehen. = He may draw an extra card.

So both are correct, but the structure is different.

In this kind of game context, nachziehen means to draw an additional card or to draw a replacement card.

The prefix nach- often gives the idea of afterwards or in addition. So eine Karte nachziehen suggests drawing a card after the normal action or as compensation.

The exact translation depends on the game rules, but draw another card is often a natural English rendering.

Eine Karte is in the accusative case because it is the direct object of nachziehen.

The verb answers the question what may someone draw?

• eine Karte

Because Karte is feminine, the nominative and accusative forms of eine look the same:

• nominative: eine Karte
• accusative: eine Karte

So you cannot see the case difference in the article here, but grammatically it is accusative.

Grammatically, wer is treated as singular.

That is why the verbs are singular:

• Wer aussetzt, darf ...

Even though English may translate this as those who or people who, German still uses singular verb forms with wer in this kind of sentence.

So:

• Wer kommt, ist willkommen.
• Wer aussetzt, darf eine Karte nachziehen.

This is normal German usage.

Yes, that would also be possible, but it is a slightly different structure.

• Wer aussetzt, darf eine Karte nachziehen. = Whoever skips a turn may draw a card.

• Wenn man aussetzt, darf man eine Karte nachziehen. = If you/one skip(s) a turn, you may draw a card.

The version with wer sounds a bit more like a rule applying to any person who meets that condition. It is very natural in instructions and rules.

The sentence has two parts:

1. Wer aussetzt

   • subordinate clause
   • verb at the end

2. darf eine Karte nachziehen

   • main clause
   • finite verb in second position

A useful way to see it is:

• [Wer aussetzt], [darf] [eine Karte] [nachziehen].

The whole first clause counts as one unit before the main clause, so the main clause still follows the usual verb-second rule.