I Need Battery Choice Help?

A question; Front wheel drive is fine for product made for it. Non ebike bicycle forks are not designed for the continuous load that a motor puts on them. Rear drive with the strength that the triangle affords are no problem. Have there been any failures of front forks using a retrofitted motor?
I have a controller that is rated at 13ah!
What battery shoud I get?
I think you be confused with terminology. Ah typically refers to the amount of power a battery can provide to the system. Controllers speak of Amps and Volts.

What you need to know is the voltage the controller can handle choose a battery with that voltage and then buy a battery with the largest Ah rating you can afford. Also when looking at batteries its very important to know whose cells the Mfg is using when building the battery. I would stick with Samsung, LG, Panasonic.
On the front fork question, HELLL YES!!!

Unfortunately, some of those who have experienced this are no longer able to respond.
Based on your other question regarding your controller, you need a 48v battery. The Ah rating is one I'd spend as much as I can afford. Before that tho, does the new battery fit on the bike without any new wiring issues... I'd go on a diatribe about battery sizing and what kind of measurements they are using in China but i've already said enough :)
Wait, you are saying that they use actual measurements in China? I thought they just had a piece of string with some knots in it.