I'm not a Peltier expert and I think they are non-linear*, but it says 7A and 1.7 Ohms, and that's 12V (Ohm's Law).
You're going to need a BIG battery for 7 (or 14) Amps, especially if you need much running time. Are you using a car battery? (Heating or cooling takes a LOT of energy!) Check the Amp-hour rating on the battery. And in case you don't know this and you have to convert, 1 Amp-hour is 1000 mA-hr.
You "schematic" is wrong because the relay should be in series with the Peltier.
If you wire 2 Peltier devices in series you need to double the voltage. If you wire them in parallel, you'll need twice the current.
A relay has ratings for the coil and for the contacts. Relays with 12V coils are common. Since you only get 5V at 40mA or less out of the Arduino, you'll need a driver for the relay. You can get relay boards with a relay and driver mounted on the board. The coil specs are "exact". A 12V / 100mA relay coil should be operated from 12V and it will draw 100mA.
The contact specs are the maximum rating... You can use a relay rated for 230V @ 10A in a 12V / 1A circuit.
For 12VDC, a MOSFET is an alternative to a relay (and you can get "logic level" MOSFETS that can be controlled by 5V from an Arduino).
Or, you can get a solid state relay that's controlled by 5V (at low current) so you can control it directly from the Arduino. But make sure you get one that's rated for DC, because most AC solid states will latch-on with DC and you can't turn them off (without removing power).
- I think the resistance changes when the applied voltage changes, like a diode. Increase the voltage by a little and the current goes up a lot.