The easiest and best method for removing paint from concrete is to use a mechanical grinder or a wire brush. This method will guarantee that the surface will be free of any paint. It is a dusty job, so be sure to ventilate the basement well and make sure that you wear a mask. If the floor is not perfectly flat, even it out with a self-leveling concrete mix. For the tile adhesive, my suggestion is that you speak to the professionals at a tile manufacturing center. Each type of tile requires a specific type of mortar, and the tile experts would know which adhesive or mortar works best with your tiles.