The basic answer is You have your process wrong, at least the concept of the process.
I need to prepare them for print and after converting them to CMYK in Photoshop CC
The images should not be prepared for print after converting them to CMYK.
They should be prepared and adjusted, on a color calibrated workflow in RGB, and the very last step is to convert them to CMYK.
The black parts are above 300% and needs to be fixed
No, you simply chose the wrong color profile. You probably used one like Fogra 39 that has a maximum ink TAC (Total Area Coverage) of about 330%. Use one like SWOP 2 that has a 300% TAC.
Your provider should tell you what profile to use and what is the TAC they use, some actually can use a TAC of more 300%.
Their color saturation (black parts)
A tip. A black is not color saturated, a saturated color is a bright red, a pure yellow, etc. A nonsaturated color is gray, white and black. You are refering to saturation of ink, not color.
Another way would be better?
The workflow is:
- Calibrate your monitor
- Use the right CMYK color profile
- Prepare your application to use this CMYK color profile to simulate it on screen so you made the adjustments on how you want the print to look like when converted from RGB to CMYK and printed.
- Convert the image using that color profile and the colors and ink amounts should be right.
- The printer should follow the ISO specification to achieve the correct color.
- It is highly advisable that they provide you a color calibrated hard copy of it to be signed and used as a visual reference.
Is there a way how to remain the black color in the picture more sharp...
Again, you are mixing concepts. Sharpness has nothing to do with black, or any color for that matter, sharpness is how the edges of an image are seen compared with the surrounding area.
I start to think, where is the idea?
A color calibrated workflow.
An important note: Preparing files for a magazine is not a trivial task. You are potentially facing a big economic loss. Have a professional to double check this files prior to print, including the printer and have the color calibrated hard copy signed and authorized by the final client.
This hard copy is not exactly the same color than the final product because is using a different system and the print itself has some variations, but it should be into a reasonable range.