Chosen Solution

Can TrueDepth camera system (or FaceID) works after removing only the front camera while the rest of the components (infrared camera, flood illuminator, proximity sensor, ambient light sensor, dot projector) is installed?

No, the Face ID will not work if you remove the front face camera. But if you replace the front face camera with a new one, it will still work.

No, faceID is a combination of both depth and visual comparison.