Convert the RGB colors to CMYK colors in Photoshop with:
Change the DPI to 300 in Photoshop with:
In the Image Size settings:
Resample Image if it's checked, so your image stays the same size (pixel dimensions stay the same).
Note that your file has colors on the edges and requires a 3 mm Bleed on it so that you get no white edges after cutting the edges.
This can't be done with Photoshop and would require Adobe InDesign. However, you could cut it a bit on the colored edges so that the business cards get a little smaller. You lose size but have no white edges (which is why bleed is required).