Electronic – 4 layers Design- Using polygons

1.- Grounding for 2 layer PCB is a really difficult point. If you cann't use Bottom layer for a GND plane, you have to use a ground grids. With this technique you want to create a grid of ground in bottom layer. It will work like a ground plane. It's a difficult technique to explain in this post.

2- It depends but it's probably that 0603 capacitor have a lower ESR and a lower ESL.

3- You have to consider the "skin effect" for high frequency. At these frequency current flows only on the surface of the conductor. It's for that reason that you can consider the "botton side (ot the top side) of the third layer" o the "top side (or bottom side) of the second layer". It's a messy way to speak.

Regarding the image you refer. Probably second layer is ground and third layer is a Power, but we don't know. We know that they are planes and the return current flows in nearest plane, regarless it's a ground o power.

If you prefer you can symplify the image with this:

return current on top surface of layer 2 = return current on layer 2 return current on bottom surface of layer 3 = return current on layer 3

Talk to your board house. Don't assume you know the best way for them to handle this.

Basically you seem to be asking for a plated-thru milled hole. The first answer is to avoid that. If you really can't, the second answer is to ask the board house how to specify it. There are different processes, and it depends when the plating is done relative to the routing. This may require a additional routing step, which may cost extra. Again, see the first answer.