We can round that up to 3 hours and if we go with your upper limit of 600 mA, you would need:
``"600 mA" * "3 hours" = "1800 mAh" = "1.8 Ah"``
Keep in mind that this is just for the motor for the duration you specified; if there is some electronics that's on all week controlling when the motor turns on and off, you'll have to factor in how much energy that will need.
Your post looks sloppy and lazy, making it difficult for anyone to help you or to want to help you. For instance, I suspect you are not actually trying to run a 12 V cell-phone charger off of your phone battery. But even if I assume you want to make a portable power pack into which you can plug in your phone charger, I still cannot really understand your question. What are you trying to achieve? Why do you care about efficiency? Typically, in an energy conversation, the relevant efficiency is how much energy you spend charging your power pack vs. what you get back out of it, but it seems like you might care more about being cost efficient or size efficient.
It is not appropriate to think about an "is it okay" question based on the specs you have given. You can use the current and voltage specifications of the chargers to get a rough best-case estimate of how long it will take to charge the batteries, but whether it will work at all or be safe is a completely separate issue. You should only use chargers that are specifically made for your kind of battery pack (and you should make sure you know how to configure them appropriately).
Sorry, I am not familiar with those Kyosho 4-wire servos. By the way, once we are dealing with a proprietary system like this, we don't know what the first 3 wires are, either (though power and ground are good guesses for two of them). If you (or anyone else reading this) have a broken one that you would be willing to send in, I would be happy to take a look at it.
More Ah will just last longer, and since you don't need much, it seems like the primary consideration should be size or weight. Separately, though, I think this 12V battery->inverter->AC adapter route is quite awkward. You can probably get by with just using AA batteries. You could either set up your own battery holder or get some AA to C battery adapters, which are just sleeves or shells that fit around AA batteries to make the final diameter match that of C batteries.
You start out ok, up through where you got the 20 mA, but then you got sloppy with the units in exactly the way this blog post was supposed to help people avoid. 20 mA is already a rate, and as long as that fan is running, the current is 20 mA, and it is wrong to say 20 mA per hour or 10 mA for 30 minutes. It would be correct to say the battery will deliver 10 mAh in 30 minutes.
I've crossed out the incorrect parts in your comment in the hopes that it will help others avoid this kind of mistake. The 65 hour result based on the starting assumptions is right, though.
As a rough approximation (within a factor of two), I would expect similar battery life. The main thing I'm skeptical about is that 5V is not a natural voltage for a lithium ion battery. If there's actually a 3.7 V, 2600 mAh battery inside and the converter to 5V is 90% efficient, you'd be getting the equivalent of about 5V, 1750mAh.
I don't know enough about your system to know for sure. There's got to be some limit on your alternator and whatever battery charging circuit is in your car, and while my impression is that lead acid batteries are among the more forgiving regarding charging, you still might limit their life or otherwise damage them if you just do what you are proposing.