Learn Icelandic: Hver er í veislunni með okkur?

The preposition með requires the dative case when it means "with" in the sense of accompaniment (being together with someone). okkur is the dative form of við (we), which gives us með okkur for "with us".

Why is the word for "party" written as veislunni?

The base word is veisla. Here it has the definite article attached to the end to mean "the party". Because it follows the preposition í showing a stationary location, it must be in the dative case, making it veislunni.

Would it ever be í veisluna instead?

Yes, but only if there was movement. The preposition í takes the accusative case (veisluna) when moving towards a location, like going to the party. Because we are asking who is already stationary at the party, it takes the dative case (veislunni).

Does Hver always take the singular verb er?

Yes, when asking "Who is...?" in Icelandic, Hver acts as a third-person singular subject. This works exactly like English: we ask "Who is here?" rather than "Who are here?", even if we expect a group of people to be to the answer.