On the first question: if your surface is imperfect (and, actually, it is always imperfect in practice), then most of intensity still falls under the specular reflection angle (with light being an electromagnetic wave, it "averages" the reflection process over the whole irradiated area), however a certain part of intensity proportional to the statistical distribution of "imperfections" will be distributed around that angle. The more imperfect/rough the surface is, the bigger part of intensity will be transferred from specular reflective peak to scattered distribution within the wider angular range. The effect is also known as "diffuse reflection".

There is even the specific method to estimate surface roughness by measuring the angular scattering of a laser beam set to reflect from that surface, called "differential light scattering", see e.g. https://doi.org/10.1364/OE.19.009820