Yes, you would nip each intersection after you sewed all the seams in one direction. That way you will be able to offset the seams in opposing directions, and eliminate a lot of the bulk when you started sewing in the other directions.
The formula for HST blocks is the FINISHED size plus 7/8" for the two starting squares.
Are your solid blocks on the grid finishing at 2" - so you're actually putting down 2.5" squares of fabric?
Or are the solid squares 2", and finishing at 1.5"?
Either way, I would cut larger starting squares for the HST blocks, make the HST's, and then trim down to the exact UNFINISHED size required.