Using 4 AA batteries to charge mobile phone
your approaches

won't work – the LM7805 is so ancient, that it's voltage drop at reasonable charging currents will be &gt; 1V (and that would be bad already if your alkaline batteries are totally fresh and not half discharged. Also, using a linear regulator in a battery-powered device is a bad idea; you'd be wasting one sixth of your energy. Use a switch-mode regulator instead.

no, AA batteries can easily supply several amperes of current. So, while twice the amount of cells doubles the capacity of your energy storage, it's not necessary for current reasons.

Now you're crossing into totally senseless land: use a switch-mode supply to regulate up, and a linear one to regulate down. That makes no sense. Simply directly use a switch-mode supply architecture for AA voltage-&gt;USB voltage. Switching up to 15 V and then using a linear regulator to go down to 5 V wastes 10 W of power if your charging current is 1 A. That's twice as much as the power actually used for charging.  This is so inefficient that I'm willing to say, no, this won't work.


questions

your first system won't work, your second is not necessary, your third is a bit... stupid, sorry.
no, the current sourcing ability of AA batteries is quite good, actually.

So, simply use four AA batteries to get 6V, and then use a Buck converter to go down to 5V.
However, there's a reason why power banks use lithium batteries: these have a higher energy density than alkaline AA batteries, so you might be pretty disappointed how many batteries you use up just charging your phone once.