Stranded vs Solid Copper

I assume the other 5 outlets and light are wired with Romex 12/2  if it's a 20amp circuit back to the breaker box. I guess using 4 or 5 feet of stranded at the end of this run might make a sonic difference but I really don't see how. You can use stranded and it is more flexible though it should be terminated at the outlets slightly different than solid to keep the strands tight. 

The electrician should have used an extender or spacrs to make the receptacle tight not simply use the face plate screw to hold it but nothing new there. The patio home I moved in this year I went around and had to fix about half the receptacles and switches with spacers to tighten them. 

Not getting the point of a home made box, hospital grade receptacles will fit in standard boxes. Not  sure home made would meet code might want to check on that, if there was an accident insurance companies can get a little testy  on such things. 

You can get outlet extenders and / or spacers to keep the receptacle from pushing in and breaking the face plate. You could remove the old box and install a double gang if you want 2 receptacles in that location or install another box and run a wire from the existing box to your new box if you want them in seperate locations.