If you mean flash red, it does that when focus is achieved and the light levels are low (there's a setting that controls that - AF point illumination can be off, on, or auto - yours is set to auto).
Yes, if you want to focus-recompose, you half-press the shutter with the selected AF point on the subject, then recompose, then shoot. It's a bad idea from the center point with fast primes shot wide open, because it results in backfocus. You may still need to even with the 5DIII, if you want the subject outside of the AF point spread, but start with a point at the edge, not the center.