Color is usually applied to an image in Photoshop.
The only kind of images you can color in InDesign are grayscale images without transparency in formats like TIFF or JPEG.
No matter what you do, InD will always show the CMYK plates for printing, even when empty.
If you make the graphics with 2 color, and are using the same PMS swatch (you can export the PMS colors from InD or PS as a swatch library .ase and import to both apps to ensure they are exactly the same swatch) you would just need to tell the printer to only use 2 colors and ignore the empty plates. 9 times out of 10 they would know that anyway. I would be more worried if you were unable to delete any CMYK swatches out of the InD swatches panel, as then you would need to find those colors and change or remove them.
In ID you can use the Ink Manager to alias one spot color to another so having multiple spots is not a problem, but there is no way to convert a process color to spot, before or during output/export.
You can easily find process colors in the document either of two ways:
Turn on separations preview and turn off visibility of the Spot and K plates, and anything still visible is using C, M, or Y, or you can set up a Preflight Profile that flags the use of C,M or Y plates, and the Preflight panel will list the errors and provide handy links.
If you have process colors in your imported art you have two choices -- fix the original and reimport, or convert the process color to spot in Acrobat Pro. This is doable but a long way from intuitive, and well hidden, in Preflight, where you can add a single fixup to convert any specific CMYK mix to a spot color.