I've already made sure that all imported images are in CMYK mode (by previusly editing them in Photoshop)
This is unnecessary. Leave the images RGB. As mentioned in the previous post you can convert to CMYK when you output a PDF.
I know how to export PDF in CKYK mode (by choosing PDF/X-1a:2003 standerd, right?), but how do you get and save entire indd file in CMYK mode?
InDesign is not like Illustrator and Photoshop where you are restricted to one color mode. CMYK and RGB can coexist in the same document.
To see CMYK in InDesign, you need to utilize Separations Preview. This is very important. Also in Swatches panel, go to Ink Manager and select "All Spots to Process" This will eliminate any spot plates – if you had any spots, they will be removed from Separations Preview. If you actually need certain colors to remain spot, in Ink Manager, click on the icon to the left of the color name to change it back to spot.
To expand on what the previous poster stated: In InDesign go to Edit: Assign Profiles. You will see that the document has both an RGB and a CMYK profile. You can't make it one or the other, it's always both.
Note the document profiles can be different from those seen in Edit: Color Settings. The profiles in Color Settings affect untagged documents and new documents. They do not affect pre-existing tagged documents.
If you want to see if you have any RGB colors being used in InDesign, in Swatches panel go to "Add Unnamed Colors." Refer to the color icons in the list, any RGB swatches will have the RGB icon. Not the end of the world if you have them, they can be converted to CMYK along with RGB images when you output a PDF.
Normally for print design, you want the document transparency blend space to be CMYK (under Edit: Transparency blend space).
Hope this helps.