Sound like water in the electrics or plug leads giving misfire that goes as it warms up, my S1 Roadster was a bugger for that.
I have driven a mates +4 GDI and the behavour isn't normal . It doesnt happen on my CX which has BMW GDI engine.
My CX hadn't been driven for 9 months & pinked at high throttle but clean fuel & injector cleaner helped to resolve that.
I would also add a fuel stabiliser like Stabil in case there is dross from old fuel in the tank.
