How to get rid of background and change the color of detailed lines (floor plans)?

confused unicorn,

Further to what Luke and Met said, I believe the original was black artwork on a transparent background.

That was created in some form of vector art once, if quality is an issue for you, see if you can get that.

How can I place detailed image (like floor plans) into indesign?

Can you get a vector version of the drawing? this is almost always preferred over a .png (raster image). If you have a vector file, you may be able to open and edit it in Illustrator, changing the fill and stroke colors as needed, save it as an .ai or .pdf then place it into an InDesign file.

How can I change the color of floor plan without background?*

If you are editing a vector file in Illustrator, create a swatch of the desired color, select the existing line color and apply the swatch*. 

If you have no other option but a .png, you can open it in Photoshop, adjust the image so the lines are solid black only (Image> adjust> curves, and/or Image> Adjust> Channel mixer) save it as a grayscale .tiff (Image> mode> grayscale).

Place the .tiff into your InDesign file, using the Direct select tool (white arrow) select the .tiff and apply any swatch color to it, including white.

*tip: if you want the drawing to be white, create a new layer in Illustrator called "background" and add a fill color, just so you can see the white drawing above, save as a layered .pdf or .ai. Once placed into InDesign, use Object> Object layer options to turn off the unwanted background layer.

If the quality of the image you want to use is similar to what you showed here, Image Trace will not give good results.

Editing (inverting) and coloring would best be done in Photoshop.

Hi as i think first invert the colors of this image so your drawing become black then image trace and do what you want in layers rest all depends on your image from autocad it should be high resolution too...regards