Learn Romanian: Voi aveți un câine mare? - Do you all have a big dog?

aveți is the specific form of the verb a avea (to have) that matches voi (you plural / you all). So voi aveți translates to "you all have".

There is no word for "Do" in the Romanian sentence. How is it a question?

Romanian doesn't use helper words like "do" or "does" to ask questions. You just take the standard statement—Voi aveți un câine mare (You all have a big dog)—and add a question mark at the end. When speaking, you simply make your voice go up at the end of the sentence.

Why does mare (big) come after câine (dog)?

In Romanian, adjectives almost always come after the noun they describe. Instead of saying "a big dog", you say un câine mare, which literally translates to "a dog big".

Would mare change if the pet was a feminine noun, like a cat (pisică)?

No, mare is a handy adjective because its singular form stays exactly the same for both masculine and feminine nouns. So it is un câine mare (a big dog - masculine) and o pisică mare (a big cat - feminine).