These are very good questions, because they force one to realize that the boundary between Classical and Quantum Electrodynamics is still conceptually discontinuous, even though most phenomena can be "correctly" understood either way.
In Classical Electrodynamics, electric and magnetic fields are continuous and the media in which they propagate are either continuous or are composed of classical particles behaving like tiny billiard balls with charge. In that picture, an incoming electromagnetic wave makes the charges move, and moving charges generate outgoing electromagnetic waves; the whole process of "reflection" can be understood in these terms where nothing is lost or created. The waves wiggle the medium and the wiggling modifies the waves in return. Nothing is instantaneous, it is all continuous. This picture works quite well as long as you don't ask how lasers work in the first place, or allow any excitations of the atoms of the medium.
In Quantum Electrodynamics (QED), electromagnetic waves come in quantized packets called "photons", which are just like any other elementary particles in many respects. These "particles of light" have only one type of interaction: they are either created whole or annihilated completely at each "vertex" on the little cartoon depictions we call "Feynman diagrams" after their inventor. You may have seen some; if not, Google them! Anyway, in this picture the photons of the incoming beam are absorbed and reemitted by the electrons in the mirror. The details are governed by QED, the rules of which are elegantly embodied in the Feynman diagrams and the integrals to which they correspond.
The easiest way to think about "reflection" is to imagine the photons are little billiard balls bouncing off cushions on a billiard table; but of course this "quasi-quantum" picture ignores the fundamental nature of photons (to be created or destroyed only). The hardest way is to use QED to calculate amplitudes for the quantum processes; this would be the most correct and accurate, but might take a lifetime to understand fully. In between is Classical Electrodynamics, which is absolutely wrong but approximately right, and thus very useful.
Still, QED obeys a few simple principles like conservation of energy and momentum, which should be familiar to everyone, and which go a long way toward explaining the basic behaviour of the processes depicted by the Feynman diagrams, like "reflection".
I hope this is appropriately confusing, while tantalizingly revealing.