How can I finish and seal an interior exposed brick wall?
A sealer I use for stone and grout (also rated for brick) is Miracle 511 Porous Plus.  It is solvent based, so use an organic respirator during application, remove pets, ventilate! 

The Miracle product adds no sheen or color, absorbing completely.  

They have a water-based product also, although I haven't used it and can't confirm-or-deny. 

The Sure Klean is an acidic product, (hydrocloric acid).  On exteriors, you would flood with hose and/or pressure washer, obviating the need for a neutralizer.  I doubt you would hose down your interior, so a neutralizer indoors is needed.