[Myka]

Halimeda can actually be very invasive sprouting up all over the place. It is easy to remove, but getting every little bit is the difficult part, and every little bit will carry on growing. It is not something you want in the display tank. The red algae I can't see well enough to ID...is it easy or difficult to pull off the rock? Generally, if it isn't Coralline then it is a "bad" algae to have in the display tank. Most macroalgae even when introduced purposely (like Caulerpa or Halimenia, etc) can easily become invasive. Imo, unless you're aiming for a planted tank rather than a coral tank, the only algae allowed should be Coralline in the display and Chaeto in the sump.

From the photos is looks like your tank has a bit of a nutrient load. Manual removal followed by improved nutrient export would be your best long-term solution. This can be achieved by using a good quality skimmer (or upgrading current skimmer), growing Chaeto algae in the sump, algae scrubbers, removal of detritus during waterchanges, replacement of filter medias more often, use of GFO and/or carbon, gradual removal of any biofilters (like bioballs, biowheels, ceramic rings)...