Noob question: Understanding power

Is that understanding correct or completely wrong?
Could I mix the 2 to give me more max amps and a higher voltage with the same number of batteries?
For instance: 3 AA batteries in parallel giving me 5.4A maximum and then connect this in series to the last battery, will that give me 5.4A max with 3v?

First thing to try and completely understand is that the maximum current capacity or any power supply or battery is just it's rate maximum capacity to supply current. Just like you house power outlet can power a 7 watt night light or also a 700 watt vacuum cleaner, it's the load that determines how much current will flow from a fixed voltage source, it's an Ohm's law thing. So the actual amount of current that will flow from your voltage source is a function of the load resistance attached to it, or in your case the current demand that the servo(s) will try and draw. A servo at rest may only draw a few milliamps of current, but when commanded to move they will draw more current and if trying to supply maximum torque to a mechanical load, still draw a higher current. The 1 amp per servo is just a general rule of thumb as the true system current will depend on number of servos, the specific model of servo, if they will be commanded to move all at the same time and what maximum mechanical load they have to try and move. So there is no simple answer to how much current capacity your specific servos and application will require. The 1 amp per servo rule is a good starting point at least.

Basically this all boils back to me trying to power the arduino board + 6 servos off 1 power source. Each servo needs 4.8v-6v (a quick google indicates each servo should have 1A so it can operate to it's maximum potential under load) so I'm trying to figure out exactly how I can power this without having to use non-standard batteries or without having to have a lot of batteries.

To add to the complexity of your question, batteries don't maintain a fixed voltage over the life of their discharge curve, but your arduino does require a regulated +5vdc voltage source (at least it has to never see higher then 5.5vdc or risk damage), while your servos can handle a range of 4.8 to 6 vdc. Also when selecting batteries you have to have a decent handle on the total current draw during normal operation and how long you require the batteries to power the project before having to stop and recharge them.

I hope that makes sense and the questions aren't too ridiculous. I really appreciate any help or advice you could provide because, like I said, I'm a hardware noob!

Those are good questions for a beginner, but as I hope you see there is no simple answer but rather a series of trade-off decisions, and we haven't even talked about cost limits or volume size limits if to be mounted inside something, and lastly what the charger requirements are going to be. Non rechargeable batteries make no sense at all in a servo based project, just throwing money away with each use.
Lefty