Was cleaning my fans, screw touched motherboard got a spark, bought..

It is unfortunate that this has happened to you. When cleaning out fans in a computer, especially a laptop, it is a good idea to make sure to remove all power (power cord and battery) and let the computer sit for at least 10 minutes to let all the capacitors drain down so that the chance of a short like this happening is almost zero.

Without being able to inspect each component individually it is really difficult to narrow down exactly what is faulty from the short crated by the screw coming into contact with the two exposed pads. What I can tell from the pictures provided is that part of the systems VRM (Voltage Regulator Module) which controls and stabilizes the voltage provided to components on the motherboard, primarily the CPU, GPU, and RAM being the big ones. If a component in the VRM fails, in this case due to a short, then the voltage provided to one of those components may no longer be provided at the proper level and can cause instability or failure of the component that is being provided said voltage.

From your picture the modules labeled PQM, PLM1, PLM11, CD32, and the 6 surface mount capacitors are what make up the VRM circuit and any number of them could be damaged or failed. The other concern is that whatever they are regulating could be damaged as well. From the location of the VRM to the ENE power management IO chip I would guess that it was damaged and would help explain your battery issue as it can no longer regulate and manage the power delivery to the system. This could also explain the shutdowns when loading up a game that would cause the system to try and draw more power and not be able to get it.

You could try replacing all the surface mount components within this VRM and the power management chip but you will likely have to replace components on the back side of the motherboard as well as the circuits quite often bounce back and forth between the sides of the board. If you have the ability and tools necessary to replace them you can definitely try. Most repair shops are likely to tell you that you just need to replace the motherboard to be sure that you don't miss any damaged components (this would be my recommendation as well).