Technical 1.2 L 8v stutter at <1500 RPM

[TotalnoTito]

Hi, I've recently bought a 2002 Punto with a 1.2 L 8v engine. I've noticed that the car stutters badly when below 1500 RPM, and ESPECIALLY in 2nd gear. It also "shakes" when idle. It doesn't lose power though.

What could be causing these issues? Head gasket? Fuel filter? Spark plugs?

I have also noticed that the engine block is oily and leaks from the valve cover gasket

 

[George1982]

It definitely needs a cover gasket , easy job.
Take off the throttle body and clean it especially the back where the idle valve is mounted. If it doesn't help,you might need an new throttle body assembly.
You should consider replacing the spark plugs and the cables,if they are old and downgraded.