Thank you very much usedranger, you sure took a lot of time helping
. I ended up with the Permatex 24115 silicone formula, the one I linked.
I managed to take out the piston by connecting it back to the brake hose and pushing it out. No corrosion at all, nothing wrong with it, as far as I'm concerned. I cleaned it up and reassembled it, mounted everythig back on the car ... and surprise ... no change
I'll check the brake hose next as RahX suggested.