How to deal with the backup data wire may depend on the exact pixel type.
I saw a Ray Wu seed pixel listing just the other day that advised to connect the 2 data wires together at the source.
You could put a 3A diode in series with channel one (anode to controller, cathode to +ve of connected load) so that at worst it would output pulsed DC and not reverse polarity whatever you're feeding.
I thought they were Bluetooth? Does it say wi-fi on it anywhere?
EDIT: it does appear to be Bluetooth only, so unlikely to have an appropriate module inside.
A rough guide to current carrying capacity is 10 Amps per 1 square mm. So a 2.5mm (cross sectional area, not diameter) wire can carry about 25 Amps.
This works well for shorter distances, but beware of voltage drop on longer runs. For 240V power losing a few volts over a 10m run is no big deal...
I'm not certain that this particular MFC can be easily bypassed.
It seems to use a variant of the polarity witching method normally seen with 2 wire light sets.
Power supply brands other than Mean Well may be ok as long as they have data sheets with the relevant information available. I can speak for cold weather (we don't get it where I live), so will leave it to others to comment on that.