Electronic – Net names aren’t shown in EAGLE PCB layout

Create a footprint with GND and AGND pads. Draw copper between these pads. Yes, this will produce a DRC "Overlap" error as shown below:

This is OK. There three buttons at the bottom:

• Clear all
• Processed
• Approve

"Clear all" will temporarily clear the list for this run of the DRC. I'm not sure why that's useful; just close the window if you want it shortened.

"Processed" will fade out the color of the red X. This is potentially useful if you're iterating through a long list of DRC errors and fixing them as you go; you can keep track of the ones you think you've corrected.

"Approve" is the only one I use on a regular basis. This moves the error from the errors list to the approved list:

and keeps it there on subsequent runs of the DRC. Note that this only moves this specific error with this specific pair of nets at this specific location. Closing this window and running the DRC again produces the notification "DRC: 1 approved errors"

and no "DRC Errors" dialog. You can get this dialog back by creating an error, or (preferably) the errors command, the yellow exclamation point in the above screenshot, or the menu Tools -> Errors.

The "Approve" functionality exists for a reason, the same reason that we have tools like

#pragma GCC diagnostic ignored "-Warning"

Sometimes, it's OK to ignore a DRC error. This is one of those times.

Yes, one of the reasons for using 2-layer PCBs is to avoid the jump wires. On a complex board there would be lots of them in all directions. Your layout doesn't need the second layer, though; it's still simple enough to be routed on a single layer without wire bridges. If you get stuck you may have to move some components to another position, but it can be done.

I would suggest to try it instead of going the easy way of the 2-layer board. It's about practice. If you don't succeed in doing this on a single layer, you'll never be able to do a more complex board on a 2-layer PCB either.

A professionally made multilayer PCB will have copper-plated vias to connect the top trace with the bottom trace. If you plan to make the PCB yourself you won't have the through-metallization, but since you only use PTH parts you can solve that by soldering the wires on both sides of the board. For some components the wire may not be reachable on the component side. Just make sure there's no trace to the hole on that side then. If you would need vias apart from the components' mounting holes you can solder a thin wire on both sides of the hole.

2-layer PCBs will often use both layers for routing, and even component placement. On densely populated boards this may not leave much room for copper planes, like for ground or Vcc. If these are really required designers often will go to a 4-layer board. A ground plane not only helps in the design of HF designs, but ground is often the net with the most connections, so it takes a lot of routing away from the outer layers as well.

Today most PCBs use SMT technology, and SMDs will often be placed on both sides of the board. First the components on one side are fixed with glue dots, then the board is flipped and the parts on the other side are placed. The glue is needed to avoid the components falling of when the board is turned upside down. Some glue dot machines can place up to 50000 glue dots per hour, that's 14 per second!