Learn English – Should I say “Are you open today?” or “Do you open today?”

Many businesses have signs saying open or closed.

When a business is open, it is ready to serve customers, and the doors are probably unlocked.
When a business is closed, it is not ready to serve customers, and the doors are likely locked.

Note that closed doesn't imply anything about when they'll open again. They may never open again, or they may open in five minutes. Many businesses post schedules on doors or windows saying when they'll be open or closed.

Both words are adjectives; see Language Log for details on why open and closed are in opposition.

Declarative statements use "there are":

There are some clouds in the sky.

Questions reverse the order:

Are there some clouds in the sky?

In sentences such as "Do you know how many apples there are?" the phrase "how many apples there are" is not a question itself, it is a subordinate noun clause. The word order reversal comes in at "Do you know" (where a declarative statement would say "You do know").