In terms of the ah rating the answer would be yes. 20ah will last longer than the 12ah. It depends on whether the size of the 20ah, they are larger, will prevent you from using them.
The AH means Amp Hours and is a measure of how much electricity the battery can store. Thus if the 12AH and 15AH batteries were connected to THE SAME device (one after the other) the 15AH battery would run the device for longer than the 12AH battery.
The Ah (amp hour) rating of a battery is a measure of it's capacity. A 33Ah battery, when fully charged, will deliver 33 amps for one hour, or 11 amps for 3 hours, etc.A 7 Ah battery will only last about 20% as long as a 33Ah battery.
Both are giving the data about storage capacity of a battery. For Ex. 12V 7AH Battery will run 7 hours if you are driving the load of 1Amp continuously. But 12 12AH Battery will run 12 hours if you are driving the load of 1Amp continuously.
No. It calls for a 12AH 12v battery.
Yes. You will need a voltage regulator circuit to produce the 7.2v from the 12v source.
it depends how many hours do you want it to run, but basically 3 batteries should be enough for a little more then 1 hour
Yes, you can do this.
Yes
No
You can replace a battery with a battery of the same voltage but greater capacity as long as it will physically fit.
No, the replacement adapter has to be of an equal or greater value but never lower.
No, the new adapter will not be able to safely supply enough current.