Learn Icelandic: Tollurinn stoppaði gáminn. Af þeim sökum er sendingin sein. - Customs stopped the container. For this reason, the delivery is late.

The word sökum is the dative plural of sök, which means "fault", "cause", or "reason". Literally, the phrase translates to "from those reasons". Even though the English translation is singular ("for this reason"), Icelandic prefers the plural form for this fixed phrase.

Why does the verb er come before the subject sendingin in the second sentence?

This is the V2 (verb-second) rule. Since the connective phrase af þeim sökum takes up the first slot in the sentence, the verb er must take the second slot. This pushes the subject sendingin into the third position.

Since only one thing happened (Customs stopped the container), could I use the singular and say af þeirri sök?

No, you should stick to the plural. Af þeim sökum is a set phrase that acts as an adverbial connective meaning "consequently" or "as a result". It stays plural regardless of how many reasons or events were just mentioned.

What is the base form of gáminn and why is it in this form here?

The base word is gámur, a masculine noun meaning "container". It is in the accusative case because it is the direct object receiving the action of the verb stoppaði (stopped). The masculine accusative form is gám, and adding the definite article makes it gáminn.