A rough material reflects just as much light as a smooth one. The only difference is, that on the rough material the reflections are more scattered into all directions and not as bundled into a single direction. That gives the illusion of a highly smooth material being more reflective, but that's not true, it's just more or less "binary" as to how it reflects light (completely into one direction, nothing into another direction).
Basically a material that is highly glossy (let's say = 1.0f) would have strong reflection intensity and a material that is very rough (= 0.2f) would then have very low reflection intensity. Does that make sense, or would it be "physically incorrect" somehow ?
The only parameters needed to describe reflection are parameters to describe the materials microfacets orientations and positions (usually a single parameter called "Roughness" or "Glossiness") and the index of refraction of the material. The IOR is completely responsible for as to how much light is reflected from a microfacet which can be calculated using fresnel's equations. The easier and more common way to store this IOR is to calculate how much light would be reflected at microfacet normal incidence (aka specular intensity) and use this later on with Schlick's approximation of fresnel's equations which approximates them without the need for actual IOR values.
Each microfacet is a perfect mirror so light coming from one direction will be reflected to exactly one other direction. So how each microfacet is oriented doesn't affect how much light is reflected, only where it's being reflected to.
So overall it doesn't matter how rough your material is, the only thing that is actually responsible for how much is reflected, is the index of refraction.
You could actually derive a diffuse model from this microfacet model as well:
Simply multiply lambert with the integral over all the microfacet orientations of the percentage of microfacets being oriented into this direction multiplied with the percentage of microfacets actually visible from the light source multiplied with the complement of how much light is reflected from these microfacets (because the non-reflected rest of the light is getting scattered into the material and thus might get scattered out again into random directions as diffuse lighting if it's not absorbed).
Also I'm not quite sure what those numbers are (0.2 being rough and 1.0 being glossy). In Phong and Blinn-Phong you have exponents ranging from 1 to infinity where higher numbers represent a smoother surface and in NDFs like Beckmann or GGX you have factors ranging from 0 to 1 where higher numbers represent a rougher surface. You are either using a pretty weird NDF / BRDF or you misunderstand something.
Everything has an index of refraction and thus everything must be reflective unless it has the same index of refraction as air (or whatever material the camera is in). Skin for example is pretty much as reflective as water is (the index of refraction doesn't differ that much), but is pretty rough in comparison to water.
Also would I add the reflection to everything ? Or exclude it on materials like skin ?
metallic reflection ? How is it different ? Do I just output specular and ignore diffuse completely ? You're saying the color of the spheres in that screenshot comes from the specular color ?
Metals have index of refractions in the complex plane. If you calculate how much light is reflected using fresnel's equations, you get pretty high percentages. These are usually around 95% instead of at about 4% for dielectric materials. Also most metals unlike dielectric materials have highly varying index of refractions in the visible light spectrum. So green light might get reflected less than red light for example. Copper and gold are good examples of materials with varying index of refractions in the visible light spectrum. Also metals are highly absorbtive. The already low amount of light that is not reflected and gets scattered into the material gets absorbed so fast, that pretty much no light gets scattered out again as diffuse lighting. Keep in mind, that there is no difference between subsurface scattering and diffuse lighting.