Short answer? NO! lol
The alt puts out 14.4v. Nothing else does. It puts out a higher voltage than the batts can charge up to, so that there can be a difference of potential and current can flow FROM THE ALT into the batteries to charge them.
The reason the voltage lowered is because the alternator could not keep up with the current being drawn.
Except for the voltages you listed this statement is true.
So far so good.
No. How could this happen? IT TAKES A DIFFERENCE OF POTENTIAL TO MAKE CURRENT FLOW!!!!!!! LEARN THAT. A difference of potential is a voltage. If the alternator couldn't keep up and it's voltage dropped and now the batteries are discharging, how the hell is current going to flow from it into the batts? It can't! Furthermore, if the alternator were charging the batts and they were discharging to power the alternators, it would be totally unsustainable. Batteries discharge much faster than they recharge and they waste power when recharging. Something would fail really quickly. If the alternator can raise it's voltage above the battery voltage, all current is being drawn from it, and it is then powering the system as well as recharging the batteries.
Nope. Read above. What you're saying is not even close to correct.