anyway you think something like this could work?
N-Channel MOSFET 60V 30A - COM-10213 - SparkFun Electronics
That will work for one of the FETs, the one that pulls down, it is an N-channel one. You will also need a P-channel FET to source the power. As you want to drive 12V then the gate of this FET will have to be driven through a transistor or n-channel FET to get the 12V to 0V signal to turn it on and off.
my LED modules already have an internal resistor in order to make them work with 12V,
So again lack of information hampers a sensible reply. What LED have you got? Module, strip, component, just what?
well, it's not the best diagram I have ever seen, but still you can get an idea of the schematic
No you can't it is total pants. It is dishonest of the person to put it up and I would have nothing to do with him if it were me. At least a complaint would be going in. I assume it is a crude attempt to stop anyone copying the design, but something like that is deplorable.