Breakdown of Вы хотите остаться дома?
дома
at home
вы
you (plural or formal)
хотеть
to want
остаться
to stay
Questions & Answers about Вы хотите остаться дома?
Why is the verb "want" spelled as хотите here?
Because it has to match the pronoun вы (you, formal or plural). The base verb is хотеть (to want). When you use it with вы, it changes its ending to become хотите.
Why doesn't the second verb, остаться (to stay), change its ending?
In Russian, when you combine a verb like "want" or "can" with another action, only the first verb changes to match the person. The second verb stays in its basic dictionary form, called the infinitive. That is why остаться keeps its basic ending.
I learned that "house" is дом. Why is it дома in this sentence?
While дом means "house" (the physical building), дома is a special word that means "at home". You use дома whenever you are talking about someone's location being at their house.
Where is the word for "Do" in this question?
Russian does not use helper words like "do" or "does" to ask questions. You simply use the normal statement word order—вы хотите (you want)—and show that it is a question by raising the pitch of your voice at the end, or by using a question mark in writing.