I can not tell how the USB2UART is hooked up, but if the breakout board is silked correctly, it should be as follows:
3.3V - (Not connected)
RST - Atmega pin 1 thru 0.1uF cap
TX0 - Atmega pin 2 (RX0)
RX0 - Atmega pin 3 (TX0)
GND- Ground
5V - Vcc
I see this USB2UART has a PWR and TX LED, is there any activity on the TX when you upload?