Arduino circuit/breadboard not working at higher voltage?

Ok, good to see you're keeping busy.

  1. Your photoshop is not correct. You Vin going to an empty row (if you call the groups of 5 pins rows), and GND going to the Vin pin on the regulator. Need to slide those down 1 hole each.
  2. Power for pin 7 is going alllllllll the way around the board before it gets to pin 7. The cap to ground (pin 8 ) is there to ensure a clean supply voltage, especially
    with the 16MHz oscillator right there. The other lines show that these pins are connected to VCC, AVCC and AGND on the other side of the chip (power for the Analog parts of the chip). If you are planning on doing any analog functions, I would recommend a cap across pins 20 & 22 (AVCC) and 21 and 22 (ARef, see C4 at the top right of the schematic) for cleaner analog operations.
    "Your suggestion. is it as easy as just putting a 100nF cap across pins 7 (VCC) & 8 (GND)?" Yes.
    "after the I/O pins..before the jumper wires, tying into the rails?" Right across pins 7 & 8.

3.The series resistor, seen in the upper right of the schematic as RN2A (or RN2B) should always be used with an LED to keep from burning up your output pin. It limits the amount of current that will go thru the LED. They put an extra set of pads to allow a choice of parts. The LED turns when the output goes to 5V and either it will burn up or the output pin will burn up if left on long enough.
You don't need that LED at all - but it is the activity indicator used for the basic sketches & bootloader so you when download those you can see that the circuit is alive & well.

  1. The other crystal part - if you look closer, you will notice above C6 there is Y2 (and XTAL1 and XTAL2). What this is is 2 sets of pads; 1 set for a 16MHz crytal Q23 and its two 22pF caps, and 1 set for a 16MHz Resonator and 1Mohm resistor that is used with it. One or the other are used. You have a crystal and caps, no need to worry there.
    The Q1/XT1/XT2 are for the other uC chip that does the USB interface (vs an FTDI chip).