In Chicago, do you park casually on sidewalks in presence of cops as we do here in Milano?
No, never on a sidewalk, would get a ticket for sure.
Actually that depends on the cop and the situation. Years ago Mike Royko challenged the law. Seems he got a ticket for parking on sidewalk and parkway. Technically the cop can ticket your car if you are blocking the sidewalk (obstruction of a public way), if it is a city owned parkway (such as the parkway in front of city hall) or illegally parked on the street.. The parkway of your home is considered your property. As long as you don't turn it into a junk yard you should be OK.
A cop cannot give a ticket on private property without the property owners consent. We live across the street from a Church that has a carnival every year. When the carnival is in progress parking is nonexistent. Several years ago my wife and I went out for dinner. When we returned the street was all parked up and some idiot parked in my driveway. I called the cops and was told they couldn't do anything because it was private property. The best they could do was put a ticket on the car and I would have to show up in court as the complainant. So, I did the next best thing. I called a friend with a tow truck to come over. Evidently the guy saw the flashing lights by the car and came running over. He was happy to move his car. I was going to have the car yanked out into the middle of the street and leave it there.