Simple question. I have an AC induction motor, using a VFD for control. The default for accelerate time is 12 sec and start up frequency 15 Hz. The maximum freq is normally 60 Hz. Question is why 12 sec and 15 hz? How do you calculate those values?

The start up time or acceleration time depends upon the motor transient time or it can be said it depends on motor's inertial. Heavy the motor (i,e. high inertia), it will take more to time to settle.
Regarding the second part I believe, there are some frequency where variable frequency drive is not intended to work . Those frequencies are called skip frequency, where if VFD drive would had work it would create mechanical resonance.

generally speaking, many brand drive has auto tune functions. that is to say, the drive system can automatically set the parameters after input motor's parameters.

Those parameter values are "standard" values that according to which kind of variable speed drive you have will suit most of the typical applications, the intention is to provide the end user almost "plug&play" drive for such applications like pumps, small conveyors, etc. Lets say this factory settings should be ok for 85% applications, the other 15% applications will need to adjust those parameter according to the type of load and application you have. As Harry explained, it is all based on the torque-speed characteristics of the driven machine and the nominal output current (transient) of the variable frequency drive.

The acceleration time is depends more on the inertia and/or the torque-speed curve of the driven machine. You can accelerate mostly as fast as you like until you hit the maximum torque/current the variable speed drive can provide.
The minimum frequency also depends a lot on the torque-speed curve. If you need a lot of torque (=current) at a low speed you may need forced cooling of the motor. Sometimes the driven machine has a minimum speed due to for instance lubrication requirement.
In short, there is no rule for minimum speed and acceleration time. It all depends on the system.