Volkswagen Polo IV - 2008 VW Polo vibrates at idle and increases vibrat - GGeorge

I am the 2nd owner of a 2008 VW Polo , 1.2 engine, 69 HP. Whenever I start it up it has a very small vibration at idle(aprox 800 RPM), but if I use electrical stuff, especially turning on the AC or steering the wheel, the vibration becomes much more powerful. These vibration seem to go away if I accelerate over 1500 RPM.

Other symptoms (not sure if related).

-The alternator belt squeaks when it rains.

-Headlights and interior lights intensity trembles and the lights seem to dim for a second when the RPM drops.

-Whenever I try to accelerate suddenly or when I am going uphill, I also get some vibrations (knocks) even if the engine has over 2-3000 RPM.

-The first owner had a frontal accident so some of the parts have been changed.

Any ideas/clues to what could be triggering the idle time vibrations and if the symptoms are all related ?!