Soldering a high-power cable to a PCB

From the photos it looks like you are desiging a brushless driver for RC car , the RC car motor and batteries are sized for short pulses of high current and not continuous , so the limit in your case is not the PCB traces .

BUT anyway i will present some of the methods used :

1. Using a High or VERY high thick copper PCB (4oz to 20oz) probably the most expensive and not available anywhere

2. Copper bus bars welded or screwed into PCB

3. Copper wires soldered into PCB

4. Solder wick/Braid , this is my favorite since it doesnot required the amount of heat that the previous methods used which leads to permenant PCB bend.

MY Preferred Solution :

EDIT: Added PCB termination

Wurth Electronics power elements

or lugsdirect PCB Wire Connectors

It looks like the power cables are soldered to a metallic area reinforced with small dots. Someone knows what it is?

It looks like those are vias-in-pad. My guess is that they are stitching the top metal layer all the way through to the bottom for both good electrical conductivity and structural integrity. I would suggest to use all metal layers in the pad.