By default all fonts are embedded for every preset when you save a PDF from Illustrator. Images in PDF can only be embedded, but at the resolution specified and in the format specified. So just saving a PDF does both of these.
As for CMYK output, that’s a little vague. Any PDF can be separated to CMYK or printed to a CMYK device, so again, any PDF file will work. Some printers require that PDF files be saved with CMYK images, not RGB. If your printer requires that, then Press Ready or PDF/X-1a will do this. Talk to the printer to get t heir specific requirements. Probably PDF/X-1a:2001 is the safest format to save to.
I'm saving a PDF with a CMYK color profile from Illustrator. Why is it when it's placed in inDesign there's no inidication it's a CMYK file (under Link Info)? Is this a matter of Illustrator not including this information when saved or inDesign just not showing it for some reason. Even if the saved Illustrator file is RGB and/or EPS no color information is showing for the file when placed in inDesign.
Because a PDF can be both CMYK and RGB, since the format supports images in either colourspace. The Color Space column applies to exclusively raster image formats such as TIF, JPG, or PSD.