They do plug into standard residential outlets but require either a dedicated 20 amp circuit or 2 separate 10 (or 15) amp circuits.
Yep. There are two computer power connectors on the devices, which can be fed from one or two 120 or 240v citcuits.
I have another CT unit running in my apartment already (as well as a number of other miners). Keep in mind these devices are a bit loud in terms of a residential setting (they're about as loud as you'd expect a typical high performance rack-mount server to be), especially in a warm room when the fans fully spin up.
The CT miners draw close to 2KW (across both power cables) at full speed. Typical US residential power wires circuits with 15 amp breakers, so you need to spread them across two circuits to avoid tripping the breaker. You can run them at lower speeds to lower their power usage, but obviously thats not how you want to run them long term.
Since it didn't make sense to have it just sitting here while I arrange a sale I went ahead an powered up the unit, but have to keep it at the lowest power level (and had to slightly downclock some of my other miners) to avoid tripping a breaker here.
Runs fine.