The only effective means to control mold is to control the moisture it requires to thrive. You have solved the first problem by activating the utilities and restoring the function of the sump. Dry areas do not support mold (and mildew or algal) growth.
The fact the basement receives water infers there could be chronic moisture problems that could be improved by dehumidification. Signs of excessive moisture are condensation on pipes and cool surfaces like masonry walls, tanks, ducts, etc. If the basement remains humid, a dehumidifier is another tool that will provide long-term control.
The drywall is a pourous surface. The areas that are stained black probably cannot be disinfected, and should be removed. If the infection is limited to the bottom part of the wall, that part can be cut out and removed. Removing all affected drywall and replacing it solves the issue without chemical disinfection.
You indicate small areas of framing lumber may have mold growth. This can be disinfected by spraying a DILUTE chlorine bleach solution using a garden sprayer. It is recommended that this be followed by scrbbing using a stiff brush, detergent or trisodium phosphate solution, then ensuring the area can dry. NOTE by dilute I mean 10% chlorine bleach in water (1 part bleach in 10 parts water). Otherwise you get noxious odors, and don't really increase effectiveness.
You might want to get a small stiff brush you can attach to a pole so you don't actually have to get so close to the areas you are cleaning. Do not spray near any exposed knob and tube wiring or electrical service. Combined with dehumidifier, this should be enough to end the problem. Once the wood has dried, you can optionally paint with a stain blocking primer such as Kilz 2 Latex or Zinsser BIN or Cover Stain Primer. These products will cover and permanently seal any water or residual mold stain. As long as any active infection is killed with the bleach solution first, this is a permanent and suitable approach to removing flood stain.
If you are not experiencing allergic reactions, the mold or mildew may not be too much of a problem. Some people are more sensitive than others, some acutely so. Mold is widely present in our environment and does not present a problem to most people. It has become an issue with the numerous lawsuits recently, so you just have to judge your ability to work with the drywall and sufaces that may or may not be mold contaminated.
When dealing with chemicals (even dilute bleach) be sure to protect skin from irritation using gloves. Safety glasses or goggles are a good idea, sunglasses are not practical in the basement LOL
Hope this helps, let me know if you have more questions.