ok, it’s monday morning, I did not expect a 2d drawing, I thought it’ was 3d 
so yes. you have faces problems. Basically, all your faces, recto and verso, are white. on a white background. then you painted a few grey. but they don’t always show.
When Xray is OFF, you have Zfighting : two faces in two groups are on top of each other, one is white, one is grey, and they both want to be seen. Sketchup picks one.
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here, the crossed part looks white. but when I orbit around, it’ll look grey.
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or it’ll look a bit of both. this is a sign of Zfighting.
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Your problem right now is that you have a white face for the floor. and everything you draw on top of it and apply materials to will fight to be seen.
a simple solution would be to delete the face of your floor :
since you set your background as white, this face has no use. you can actually see the zfighting in the selection.
here is your plan with a yellow background, so you see what I mean by “removing the ground face”. it might actually be better for you to work on a coloured background and only switch to white in the end.
Then, why did it work in Xray ?
Well, in xray, no Zfighting. all faces become translucent, so you have a grey on top of a white, it gives you a light grey.
by the way, the reason why your file was so heavy was this background image. I removed it, if you need it back, open your old file, copy it, then in your new file, choose “paste in place”.
here is the version without the background image and the ground face. it’s now 500ko.
Laarakker.skp (538.9 KB)