How Can I tell what DPI and what effective DPI and colour space my images are in InDesign?

If you have no way of opening an image file to see what colour space it's using or the DPI then you can view it in InDesign.

File>Place> and select your image. Click once to place the file.

Window>Info

With your image selected you will see the Actual DPI (or PPI) of the image shown and the Effective DPI.

The Effective PPI works to allow you to resize the image and it will show you what PPI your image will be when printed.

If you have an image that is 300dpi and you see that in the info panel, you want to double the size so you scale it to 200%, then your PPI is reduced to 150ppi in InDesign to and that is the resolution it will be printed at.

If you know your images are 300 dpi and you have resized them in InDesign and they are printing out badly then you know now to check to the Effective PPI in the Info Panel to see if that's the reason why.

The Info Panel will also show you the Colour Space, whether it's RGB or CMYK or LAB colours. (These can be converted to a CMYK or on export to PDF.)

The Info Panel will also show you the ICC Profile associated to the image.

It will also indicate what type of image it is, JPEG, TIFF, EPS, PDF et al file types.

So if you're working with some images and you have no way of opening them to check their PPI or Colour Space then just open the Info Panel and check them there.