Learn German: Ist euer Schlafzimmer hier? - Is your plural bedroom here?

euer is the informal plural version of 'your' (like 'you guys's' or 'y'all's'). You use it when you are talking to two or more people with whom you are on a first-name basis. If you were talking to one friend, you would use dein, and if you were talking to someone formally, you would use Ihr.

Why is the word euer without an extra ending like -e or -en?

The ending of a possessive word depends on the gender and case of the noun that comes after it. Schlafzimmer is a neuter noun (das Schlafzimmer) and it is the subject of the sentence, so it is in the nominative case. For neuter nominative nouns, euer takes no extra ending.

If euer means 'your (plural)', why does the sentence start with Ist instead of Seid?

In this sentence, the subject is the bedroom (Schlafzimmer), not the people you are talking to. Since there is only one bedroom, it acts as a third-person singular subject ('it'), so we use ist (is). You would use seid (are) if the people themselves were the subject, like in Seid ihr hier? (Are you here?).

How can I remember the gender of a long noun like Schlafzimmer so I get the euer ending right?