Can I install these on my basement concrete floor, or do I need to do something to the floor first, so I don’t have concrete sweating issues and possible mold?

You can install our 3/8" PowerPlay Rubber Tiles over concrete in a basement without placing anything under them. If your basement has moisture issues, you can seal the concrete so that you don't get any sweating issues. You don't have to do this if you install our rubber flooring, as the moisture will not affect the tiles in any way. The only thing you will notice if you have water issues is that salts will collect on the underside of the tiles. These salts will not affect the tile in any way and are easy to clean off.