I got it to work!
The problem was that I had connected the Arduino to the FTDI and not both the FTDI and the Power Brick. The SparkFun product page said that you can use like that, and the version from https://inmotion.pt that I have is identical so I though it should have worked.
Thank's a lot @jurah for you help!
You can choose to either reset the processor or execute an interrupt routine. Example code:
// watchdog intervals
// sleep bit patterns for WDTCSR
WDT_16_MS = 0b000000,
WDT_32_MS = 0b000001,
WDT_64_MS = 0b000010,
WDT_128_MS = 0b000011,
WDT_256_MS = 0b000100,
WDT_512_MS = 0b000101,
WDT_1_SEC = ...
Although, I don't understand where an increased power-consumption would come from when the INPUT pin is unconnected and no pull-up is active.
This part of your question already has 2 answers, so I'll just answer the "power saving part".
The data sheet says "If some pins are unused, it is recommended to ensure that these pins have a defined ...
The theory here is that an pin without a pull-up will probably float somewhere around the switching voltage. A bit of noise from the surroundings or whatever might push the pin up or down slightly, which will cause the internal circuitry to "flip" from high to low (or vice versa). All that flipping consumes quite a lot of power. The little tiny ...
Current is consumed when an input pin switches from HIGH to LOW or from LOW to HIGH. An unconnected "floating" input pin can change randomly depending on the local environment (EMI, noise, etc). That is unpredictable. The "it will consume more" is erroneous - it should be "it could consume more". The could is important, as I ...