Chopping it back, especially right after bloom isthe answer to taking care of phlox. If you don't, the middle will start to brown out- gets old and faded.

As for the grass, it's amazing how much time, money and energy we spend trying to get grass to grow in some places and not in others! If you can, water first, then try to pull the grass out. Grass-B-Gon will kill the grass and leave the phlox, if you decide you need chemical assistance.