A quick update.
I replaced the battery and now I get a very good voltage reading from the alt and bat. 14.7V +
When for a quick drive, car does the same thing.
One question: when the engine is warm, if I give it some throttle (anywhere from 10% up to 50% I'd say), the rpm will over around 1600-1700rpm as if it was in cutoff mode. Going up to 1700RPM then quickly back to 1600rpm while the ignition seams to momentarely cut, then back and forth over and over again...
What is that? I suspect the closed throttle position sensor but might be wrong... What do you guys think?