Wir öffnen das Absperrventil und füllen Wasser nach.

Because nachfüllen is a separable verb.

Its full infinitive is nachfüllen, but in a normal main clause, German splits it:

• Wir füllen Wasser nach.

So:

• füllen = the conjugated verb part
• nach = the separable prefix, which moves to the end

Compare:

• Main clause: Wir füllen Wasser nach.
• Infinitive: Wir müssen Wasser nachfüllen.
• Subordinate clause: ..., weil wir Wasser nachfüllen.

This is a very common pattern in German.

Not directly.

In nachfüllen, nach- is part of the verb and gives the idea of adding more or topping up. So nachfüllen means something like refill or top up, not literally fill after.

German prefixes often change the meaning of a verb in ways that do not translate word-for-word into English.

Because the subject is the same as in the first clause.

The full version would be:

• Wir öffnen das Absperrventil und wir füllen Wasser nach.

But in German, just like in English, you can leave out the repeated subject in a coordinated clause if it is clearly the same:

• Wir öffnen das Absperrventil und füllen Wasser nach.

This sounds natural and avoids repetition.

Absperrventil is a compound noun:

• Absperr- = shut-off / blocking
• Ventil = valve

In German compounds, the last part decides the gender. Since Ventil is neuter, the whole word is neuter:

• das Ventil
• das Absperrventil

This is a very useful rule for German compound nouns.

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

German often leaves out the article with substances and materials when speaking generally:

• Wir trinken Wasser.
• Er kauft Milch.
• Sie brauchen Zucker.

So here:

• Wasser nachfüllen = add water / top up with water

You could use an article in a more specific context, for example if you mean a particular water already mentioned:

• Wir füllen das Wasser nach.

But in this sentence, no article is the natural choice.

They are both accusative, because they are the direct objects of the verbs.

• öffnen takes a direct object → das Absperrventil
• nachfüllen also takes a direct object → Wasser

So:

• Wir öffnen das Absperrventil.
• Wir füllen Wasser nach.

With das Absperrventil, the article das looks the same in nominative and accusative, so the case is not obvious just from the form. But its role in the sentence shows that it is accusative.

In a main clause, German uses the verb bracket structure with separable verbs:

• the conjugated verb goes near the beginning
• the separable prefix goes at the end
• other sentence elements, such as objects, go in between

So:

• Wir füllen Wasser nach.

Not:

• Wir nachfüllen Wasser.

The unsplit form nachfüllen is used when the verb is not conjugated as the main verb, for example:

• Wir wollen Wasser nachfüllen.
• ..., weil wir Wasser nachfüllen.

Yes, that is grammatically correct.

But repeating wir is usually unnecessary unless you want emphasis or contrast. The version without the second wir is more natural in ordinary speech and writing:

• Wir öffnen das Absperrventil und füllen Wasser nach.

German often works like English here:

• We open the valve and top up the water. You normally would not repeat we unless there is a special reason.

Yes, but more specifically, German forms many nouns by combining smaller nouns or stems into one compound word.

So instead of writing something like shut-off valve as two words, German writes:

• Absperrventil

This is completely normal in German. Similar examples are:

• Wasserflasche = water bottle
• Haustür = house door / front door
• Autoreifen = car tire

So Absperrventil may look long, but structurally it is just a regular compound noun.

No, normally not.

The sentence joins two coordinated parts with und:

• Wir öffnen das Absperrventil und füllen Wasser nach.

In standard German, you usually do not put a comma before und when it connects two main-clause elements like this.

So the version without a comma is the normal one.