Electronic – the purpose of inserting resistors (diodes?) directly on the path of the VCC and GND lines powering a PCB

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

In the AVR Appnote on hardware design considerations on page 5:

To protect the RESET line further from noise, it is an advantage to connect a capacitor from the RESET pin to ground. This is not directly required since the AVR internally have a low-pass filter to eliminate spikes and noise that could cause reset. Applying an extra capacitor is thus an additional protection. However, note that this capacitor cannot be present if DebugWIRE or PDI is used. If not using High Voltage Programming it is recommended to add an ESD protecting diode from RESET to Vcc, since this is not internally provided due to High Voltage Programming. Alternatively, or in addition, a Zener diode can be used to limit the RESET voltage relative to GND. The Zener diode is highly recommended in noisy environments. The components should be located physically close to the RESET pin of the AVR. Figure 2-1 shows the recommended circuit on the RESET line.

I suggest you try an external capacitor of 0.1uF to ground, and a schottky diode to from RESET to VCC to act as an ESD clamp. Add a 5.1V Zener from RESET to GND, which comes highly recommended in the manufacturer's text.