Learn Icelandic: Borðið þið oft hér?

Because the subject is þið (you, plural). For Group 1 verbs like borða (to eat), you drop the final -a and add -ið when matching it with þið.

Where is the word for "Do" in this question?

Icelandic doesn't use helper verbs like "do" or "does" to make questions. Instead, you just swap the subject and the verb. So, instead of saying "Do you eat", you say Borðið þið (Eat you).

If I want to ask just one person, does the sentence change?

Yes! þið means "you" when talking to more than one person. If you are asking one person, you use þú. The verb also changes its ending for a single person, becoming Borðar þú oft hér?

Do you pronounce the ð and þ separately in borðið þið?

No, they usually blend together in normal speech. When a word ends in ð and the next starts with þ, they merge into a single soft "th" sound, exactly like the "th" in the English word "breathe" or "the".