Learn Icelandic: Eru þeir búnir með sandpappírinn? - Are they finished with the sandpaper?

Doesn't the preposition með usually take the dative case when talking about tools like sandpaper? Why is sandpappírinn in the accusative here?

You are spot on that með meaning 'using [a tool]' normally takes the dative. However, in the specific phrase vera búinn með (to be finished with a task or a consumable item), með always takes the accusative case. Because the focus is on finishing the item or the task associated with it, sandpappírinn must be accusative.

Why does the sentence use búnir instead of just the default búið?

In vera búinn constructions, búinn acts as an adjective and must agree with the subject in gender and number. Because the subject here is þeir (masculine plural 'they'), the adjective takes the masculine plural form búnir.

How can I tell that sandpappírinn is actually in the accusative case just by looking at the ending?

Sandpappír is a masculine noun. In the singular accusative, it takes the definite article suffix -inn. If it had been in the dative case (which we now know is incorrect for this specific phrase), it would have been sandpappírnum.

If I wanted to ask if they were finished sanding (the action) instead of finished with the sandpaper (the noun), would I still use með?