Learn German: Wir bleiben während des Urlaubs hier. - We are staying here during the vacation.

The preposition während (during) requires the Genitive case. Since Urlaub is a masculine noun (der Urlaub), the definite article changes to des and we add an -s to the end of the noun, making it des Urlaubs.

Would I ever hear während dem Urlaub in conversation?

Yes, quite often! In everyday spoken German, native speakers frequently substitute the Dative case (während dem Urlaub). However, in written German and standard grammar (which you need for B1 exams), you should always use the Genitive case (des Urlaubs).

Why is hier placed at the very end of the sentence?

German sentences generally follow the Time, Manner, Place rule for word order. The time-related phrase während des Urlaubs (during the vacation) must come before the location word hier (here).

The English translation says 'are staying', so why doesn't the German sentence use a form of sein (to be)?

German does not have a continuous tense like the English '-ing' form. You should never literally translate 'are staying' word-for-word. The standard present tense Wir bleiben translates to both 'We stay' and 'We are staying' depending on the context.