the one you want to use will work fine. you need to connect a jumper wire between the two negative wire contacts on the board (one from the power supply and one to the peltier/fan)....or between the two positive wires in the other diagram (the polarity doesnt matter)
no it wont trip the breaker. some 20A circuit breakers are rated for a continuous, non-stop load of 100% and some at 80% (a cheaper design meant to handle 20a surges but not constant loads)....they both trip at 20a though. i'm seeing your loads around that 80% level and not a problem. you...
yes the peltier will need a constant 6a supply but that will only put about another .6 (6/10ths) amp load on your circuit breaker because the peltier is rated at 12v and your house circuit is 120v
just use ohms law and remember that watts is real power
volts X amps = watts
12v X 6a = 72w
72w...