How to get fine DC brush motor speed regulation?
Pittman DC 24 V brushed motor with 10,000 RPM for a hobby project. The voltage I will use is battery 12 V DC, so does that mean the speed will be 5,000 RPM?

About right, unloaded. If there is a mechanical load on the motor shaft it will be slower.

I will try to find ready gearbox combination with 400 : 1 ratio because I want to get around 12.5 RPM at the shaft. (...) I want to FINE control the speed of this gearmotor with PWM around 0.0133 RPM! Is this possible to achieve at all and is this possible to achieve with PWM?

No.
You can't have good control on a motor at 1% of its rated rpm. It's designed to work in a range say 10-100% of its rated RMP. At this low rpm it will have no torque, among other problems.
If you want accurate speed control without headaches, get a stepper motor with a controller, and a gearbox. If the torque ripple of a stepper is a problem, a controller with microstepping can help.
The nice thing about a stepper motor is it's synchronous. Unless your load is heavy enough to make it slip, it will go at exactly the same speed as the control signal, so you don't need to measure the rpm and use feedback to adjust the control voltage. It can also control speed over a wider range of rpm than a brushed motor.
You can also use a cheap brushed motor, with a flywheel if torque ripple is a problem, and a gearbox/pulleys/belts to make sure the maximum desired output rpm corresponds to a bit below the motor's nominal rpm (not 1%). But in this case you will need a circuit to measure the rotation speed and feedback to adjust the PWM to keep the speed constant.