Is the value of CMYK color of indesign background and pictures with black background as the same?
Your images all use some form of Rich Black for the background, and that prints using all 4 CMYK inks. Your 100%K background will almost always seem gray next to that because it is, in fact, lighter. This will be true even if you use a profile conversion to make it also a 4-color black.
You can make your own rich black swatch and use it as the background (sample a few of the images to get some idea of a good mix), but in truth your images are still probably not going to match all that well. Images tend to have color variations across the background, and your ID background is a flat color, so even a slight mismatch can cause the edges to be obvious. There can also be differences in color on some printers caused by differences in the way raster and vector content are processesd.
I prefer to embrace that, or at least admit it is going to happen, and either use a completely different color for the background so the mismatch always shows, and looks deliberate rather than like a mismatch, or I add a stroke to the image frames, often paper, to break the continuity and disguise the mismatch.
As far as imposing the file and exporting, there are a number of free scripts, and an actual plugin, IDimposer which is also currently free, that can impose your file for you before you export. You can learn more about the plugin at Overview | IDImposer