Learn Dutch: Wij pakken het zeil en dekken de tafel af. - We grab the tarp and cover the table.

This is an example of conjunction reduction (samentrekking). Because the subject wij applies to both actions and serves the same grammatical role in both clauses, it can be left out of the second half: Wij pakken het zeil en [wij] dekken de tafel af.

Would the word order change if I chose to repeat wij?

No, the word order would remain exactly the same: ...en wij dekken de tafel af. The word en is a coordinating conjunction, which means it joins two independent main clauses without causing the verb to move to the end or swap places with the subject.

Why is af placed at the very end of the sentence?

The verb in the second clause is the separable verb afdekken (to cover). Because this is a main clause (even with the subject omitted), the conjugated part (dekken) sits in the normal verb position, and the separable prefix (af) is sent to the end of the clause.

I learned that zeil means sail. Why is it translated as tarp here?

While zeil does mean a boat's sail, in everyday Dutch it is also the standard word for a tarpaulin, tarp, or plastic ground cover (often called an afdekzeil).