Marvin, welcome to Tropical Fish Keeping forum.
With a month-old tank containing fish, the cycle is likely a major part of this problem; even if the fish get through it, they have been weakened and stressed, which can add to issues later on. You can read about cycling here: A Beginner's Guide to the Freshwater Aquarium Cycle
Second, what is the GH (general hardness) and pH of your tap water? You can find out the tap water data from the municipal water supply people, they probably have a website. This is important because different fish have different needs, and with mollies who need hard water this can weaken them seriously, adding to the problem. If you have a pH kit, what is the pH of the tank water?
Third, the nitrates. Do you have nitrates in the tap water? Always test your tap water for ammonia, nitrite and nitrate, as any of these may be present. As for the tank, what is the nitrate test result? And which test are you using?
During the 4 weeks this tank has been running, have you been carrying out weekly partial water changes, and if yes, how often and how much of the tank volume? This is critical.
The answers to the above questions will help us help you.
And the white on the mollies is most likely fungus. This is common with mollies when they are stressed, as they would be by any of the above. We can deal with this later, but we need to know the whole story.