The white flaky stuff you describe is probably efflorescence.
That indicates the presence of water seepage. Efflorescence are mineral deposits brought into the basement when water from the ground around your foundations infiltrates the basement walls. The ground around your house is probably over saturated.
The first thing you need to do is to take measures that will preventing that soil around the foundation from being oversaturated. Clean your gutters, extend your downspouts to discharge as far from the house as possible, and grade the terrain as to slope away from the foundation.
That should improve the conditions in your basement . If it doesn't, you probably have foundation drainage issues. Your home either doesn't have a french drain installed by the footing, or the one that you have is clogged, collapsed or improperly installed. You will need to provide better drainage.
You have two options to fix this.
- You can dig out the foundations and replace the french drain
- You can have an interior drainage system installed along the internal perimeter of your basement walls to collect water and divert it to the sump pump.
Both systems do the same thing: collect the water from the ground around the basement and discharge it away from it. The second method is 50% more affordable, can be installed with much less disruption, is serviceable throughout the years, and good companies will back them up with Transferable Lifetime Warranty.
I do not recommend you to apply waterproofing sealants on the interior walls as these products do nothing to dry out the ground around the foundation or keep the water from infiltrating the walls. If the drainage issue is not corrected, these products will eventually bubble up and peel off.
I would also recommend that you avoid latex paint, and not only because it will bubble and peel off, but because latex is an organic compound and combined with the typical basement moisture, favors mold growth.
As for the black stuff you say you notice in your walls, it might be mold and it is there for the same reason the efflorescence is: water seepage.
I am including a link from the US Center for Disease Control with information on Mold and how to safely remove it from your basement.
http://emergency.cdc.gov/disasters/mold/protect.asp
