Capacitor charging: do electrons migrate from the source to the dielectric?
Do electrons migrate from the source to the dielectric? No. They flow from one plate to the other plate.

Imagine a capacitor disconnected from everything, with no energy stored in it initially. This means that each of the two electrodes has a net charge of 0. For example, if each electrode/plate has million protons, then it must also have a million electrons. 

Now let’s connect a battery to the cap. What happens now is that the battery pumps a percentage of the million electronics from plate1 (connected to the plus side of the battery) to plate2 of the capacitor. This flow of charge (current) goes through the battery (since the 2 plates are electrically isolated by a dielectric), and into the other plate, until the cap reaches the battery voltage. In this sense, the electrons migrate from the source to the plate.

(Imagine the battery as a water pump, and the water molecules are the electrons particles. Yes, you can imagine these as "little rolling balls that leave the battery".)

Now once you disconnect the battery, the electrons that have already been pumped onto plate2 remain there since the two plates are electrically isolated.