Learn Icelandic: Tollvörðurinn sér það ekki. - The customs officer does not see it.

This is the 'object shift' in action. In Icelandic main clauses, unstressed object pronouns like það move in front of sentence adverbs like ekki. If the object were a regular noun, it would come after the adverb, as in Tollvörðurinn sér ekki töskuna (The customs officer does not see the bag).

Could I put the object after the negation and say Tollvörðurinn sér ekki það?

You could, but it changes the meaning. Placing the pronoun after ekki gives it heavy emphasis. It would mean 'The customs officer does not see THAT' (implying he sees something else instead), rather than just being an unstressed 'it'.

What case is það in here?

It is in the accusative case because it is the direct object of the verb sjá (to see). The pronoun það happens to have the exact same form in both the nominative and accusative cases.

How is the subject Tollvörðurinn put together?

It is a compound of tollur (customs/toll) and vörður (guard), with the masculine singular definite article -inn attached at the end. Note that vörður is a strong masculine noun that undergoes a U-shift in the nominative case.