A: It's a matter of taste.
There is no right or wrong answer to your question, it's a matter of aesthetics.
Some people like exposed brick indoors while others find it looks unfinished.
That said, painting brick (especially indoors) should be carefully considered since paint removal is a PITA and messy.
If you decide to paint it, prime with a product called SealCrete. It's a milky substance that dries clear and seals the brick to prevent moisture transfer. Once that's dry, apply 2 coats of premium latex paint. I would recommend California 2010 Exterior (yes, even inside for your application) but any quality paint will do.
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