HARDWARE QUESTION:
Ok, so I bought two 8’ INK1003 RGB strips for $24 each at Home Depot.
Everything works fine with the supplied 12v 1A power supply as long as I use only one strip. As soon as I join two strips, the strings go wacky (flash a couple times, show random colours) if I push the LEDs too bright.
What do I need to do to power the whole 16’? Do I need a 2A power supply? I don’t want to blow anything up…
The simple solution is just to choose dim colours 
Yes, you need to either use a 2 amp supply, or use both of the 1 amp supplies, feeding the power into the second strip where you join the two strips together.
You could always use a 12 volt supply capable of more than 2 amps – the strips draw what they want, the power supply does not “force” more current into them than they can use (unless something gets shorted out).
I can recommend a good switch-mode PSU supplier if you want - 12V/5A ones are petit - only 1117836 and $7ish