Is it possible for grids to have a concave cell? I mean the angle between two immediate neighboring faces in a cell is greater than 180 degrees? If indeed, is it often encountered in some widely-used commercial packages like gambit, icem/cfd, and prostar?

of course, it's geometrically possible, if the cell has more than 3 nodes. imagine a quadrilateral that looks like the head of a harpoon. it's not necessarily a good idea, though. most (if not all) algorithms have problems with such highly irregular cells. if, for example, the flow quantities are represented by a single point inside the cell, you want the boundary to nicely enclose that point.