1) If you're using tangent space normal maps, specify a UV map for your normal map node. UV is how the tangent is determined.
2) You can't really get away with using tangent space normal maps with a mapping node. Here, yeah, it's okay because you're not actually doing anything with the mapping node, not apparently. But you should know. (And Blender devs should give us a tangent input to our normal map node so that we can actually use a mapping node with a normal map node, but it's free and I still love Blender, so I can't complain too hard.)
3) Any time it's too dark, try reducing the strength of the normal map.
4) Blender handles displacement and normal mapping a little strangely, because it says, "Surely you want your normals to be your displaced normals!" but sometimes you don't. There are some hidden dependency issues involved here. I wouldn't at all be surprised if normal map node tangents did not actually use displaced normals while the normals did, which, yeah, would break normal mapping, but that's why it's called experimental.
5) Bump maps aren't bad! Use higher image bit depth, avoid lossy compression, and bump maps are fine. If you enable true displacement + bump, there's really no reason to use both a bump map and a normal map. This, I believe, is what experimental true displacement was tuned for, not for some weird thing involving the use of multiple ways to distort normals. (I don't get the feeling Blender devs use normal map nodes at all, or else we wouldn't have the previous issues I've mentioned, which have been around a long time.)
6) If you want to use normal maps with displacement, consider using a displacement modifier instead. The only thing you lose is adaptive subdivision.