Learn Icelandic: Það stendur stór refur í þjóðgarðinum. - A large fox is standing in the national park.

This is the existential það, which works similarly to 'There' in the English phrase 'There is a fox standing...'. In Icelandic, when a sentence has an indefinite subject (a fox, not the fox), you often place Það in the first position as a dummy placeholder and move the actual subject (stór refur) right after the verb.

Could I use this exact same Það structure to say 'The large fox is standing...'?

No, you can only use the existential það when the delayed subject is indefinite. If you wanted to talk about a specific, definite fox, you would drop the Það entirely and put the subject first: Stóri refurinn stendur í þjóðgarðinum.

Is the verb stendur matching the dummy pronoun Það or the fox?

It matches the actual subject, stór refur. The word Það is just a placeholder. If there were multiple foxes, the verb would change to plural (standa), but the sentence would still start with the singular placeholder Það (Það standa stórir refir í þjóðgarðinum).

Why is stór refur in the nominative case if it comes after the verb? Don't objects usually go there?

Even though it was bumped to the middle of the sentence by Það, stór refur is still the subject of the sentence doing the standing. The placeholder Það doesn't change the grammatical role of the fox, so it stays in the nominative case rather than becoming an object in the accusative case.