I have been buying mine direct from Auber,
https://www.auberins.com
I have used K type thermocouples from them, and cheap ones from ebay; no issues with either so far.
The dual channel has the same type of terminal as the single; screw clamps which work with bare wires or u-shaped fittings.
The thermocouples generally have a U-shaped crimped fitting that fits these terminals.
Yes, you'll need an adapter from AC; 12v is a pretty common voltage, should be possible find an old wall-wart from a router or something..
'Theoretically this level of creeping Orwellian dynamics should ramp up our awareness, but what happens instead is that each alert becomes less and less effective because we're incredibly stupid.' - Jerry Holkins