Hey Duane I really appreciate the reply, the ESC's do have BEC's built in (see photo- they do right?).
Yes, the ESCs do include BECs. This can be very helpful.
I am connecting the ESC's in parallel so that they will each be supplied 1.1A (2200mAh battery)
The amount of current the battery can safely provide will depend on the C rating of the battery. If the battery has a XT60 connector, it's likely made for RC vehicles so the C rating is probably at least 10. More likely, the C rating will be 20 since this seems to be a common rating for LiPo packs used in RC vehicles. The C rating should be listed on the battery.
If the battery has a C rating of 20 it will be able to provide up to 44A (20 * 2.2A). So each motor could draw 22A each. This assumes the C rating is 20. You'll need to adjust these figures if your battery isn't 20C.
The BEC's can supply 5V/2A and the ESCs are capable of taking 30A and DC between 5V-12.6V.
I assume you want to power the Arduino and servo from the LiPo pack? 12.6V is kind of high for an Arduino to use on its Vin. I'm pretty sure it's safe to bypass the regulator on the Arduino and provide power directly to the 5V line. I suggest using one BEC to power the Arduino and shield, and the other BEC to power the servo. The ground lines of all these devices will need to be connected together.
I am pretty sure to only connect one(or none see below) BEC to the Arduino otherwise it will fry... Im I correct?
It's generally a good idea not to use voltage regulators (aka BEC) in parallel. If one regulator provides a little higher voltage on the output, it will end up having to supply all the current. I'm pretty sure attempting to use regulators in parallel has caused me trouble in the past. I avoid using regulators in parallel when possible. (Interestingly when I removed the shrink wrap from one of my ESCs, I found the BEC used two regulators in parallel. So apparently it's possible to use them this way.)
Or should only the signal wire be sent to the Arduino? Especially because the Voltage will be to great for the arduino and it wont be able to step down to a manageable voltage.
You do need to be careful about what wires you connect where but it sounds like you're on the right track.