You are very close. The average power is a very accurate way to do this given that you are not pulling such a high current that the effective capacity of the battery fluctuates.
Batteries, Batteries, and More Batteries
There is one very important term, and that is the self discharge rate of the battery. This is dependent on chemistry, but lets say you get a nickel-metal hydride. The self discharge rate is
"20% or more in first 24 hours, plus 4% per day thereafter" if it is not a
low self discharge rate NiMH, which still discharges around 25 or so % a year.
Lithium batteries have some of the best characteristics for self discharge rate and my experience supports this fact. I think battery university has a great site to discuss many different battery characteristics and I often point people there to learn about batteries when they are starting to work with them. If you want to compare battery discharge rates they have an entire article discussing the phenomena.
This is a bit around the point, but I always try to make this point, when you measure battery voltage you need to have it under load. This varies with chemistry, but it is paramount in lithiums. I had a coworker placing bad coin cells in our devices and using them because the coin cells showed almost full voltage with no load. Under a load of any amount(10kohm aprox .2mA) they were flat dead.
Your Microcontroller and You
As you are dealing with using the manufacturer sheet on leakage current there are also many different issues you will have to deal with to keep to those specs that are probably also work thinking about. The biggest I have seen is a floating input. Many engineers will leave unused pins as inputs thinking, "Hey, what harm can this do?" Quite a bit if you are talking microamps. A floating input will have its transistors changing state constantly and the fluctuations cause a power draw difference. We once had a reduced lifetime in a product because we had an error that left 2 pins floating causing our standby current to more then double on our MSP430. You need to drive all of your pins to output and let them hold a state.
It is easy to miss when doing these calculations things like wakeup time. I seem to remember our MSP430 had a non-negligible wakeup time if you were doing it very often. It also had a larger power pulse for just a moment as it came online. Our little homespun RTOS had to try to take this into account and if the shutdown was less then X milliseconds we skipped it with NOPs and saved some power.
If you are looking at a very long life product, you are going to need conformal coating. The oils in your skin are not an issue immediately, but with time they form a lightly conductive material on your board. Conformal coating protects your board from this little current sucking side affect.
Read any app notes they have about low power operation, it probably covers issues like the pins need to be held as output and many other important and useful facts.
Last but not least, Dont let yourself get relaxed just because you have read the app notes and everything seems okay after a week of running your product, you have to do as clabacchio says, you must measure and make sure. You debug your code normally, this is part of it, you need to find out if you made a mistake that is causing your idle current to be mAs instead of uA or even just if you did what we did and a pin is floating on accident. Make sure you use buffered measurements when you do this, if you have a large leakage on your device taking the data you can make a mountain out of a molehill when testing. Also, never forget about pullups, they are little power hogs if you are not careful.
There is no simple answer.. Take a computer system with a 500W PSU. The sum of all parts may be capable of dissipating 1000W but utilization due to usage may only be 100W on the average. The best way is to plan for more capacity and then cost reduce later after testing it.
It is much more complicated than your suggestion. Current drawn depends on voltage, temperature . For sure you can estimate the nominal load current ought to be less than worst case load current. Unless you know something about the load curent vs voltage and determine what the Power Fail threshold when your system should shut down safely, otherwise you can let it stop in unreliable ways.
So you have no favourable measure of accuracy of predicting the operating time without experience or schematic and description to someone who understands.
We also have no idea what your design is and if you have any power fail circuit detection like the low voltage detection built into MOBO's
Sorry without more there is no simple answer to a software expert. It would be like a hardware guy telling howe many lines of unique code gets executed per minute. You could look at all the code and features and multiply by some magic utilization ratios. But the chance of it being accurate is inversely proportion to its complexity... Most like all you have to deal with is the power consumption of the top 3 items like the motors. But the the backup time is limited by the weakest link and we do not know if your power backup is balanced for each subsystem of batteries.
Best Answer
Resistance is easily calculated by the array size like 6S2P =6/2 * Cell resistance as you have done.
But good Li Ion 18650 cells might be 33 mΩ +/- 50% when fully charged and 10x this < 10% SoC so when mAh is mismatched there is increasing risk and accelerated wear on the weakest cell with the lowest mAh getting charged or discharged early thus the under or overcharged resulting in higher ESR aging. So tolerances are critical for mAh and ESR with cutoff voltage and improved lifespan with balance protection IC's.