When a car is making a turn, are its front wheels parallel to each other?

The front wheels are not parallel to each other. The reason is that when steering, all wheels are turning along circles which have a common center. Otherwise, the car would be drifting.

You are sitting in a motionless car, which is tightly sealed, i.e. no open windows, holes in the car, etc. A helium balloon on a string is tied to the floor. If you start accelerating the car, is the balloon going to move back, forward, or stay in place?

The reason the balloon floats up in the air is that the helium has a lower density, so when gravity pulls the denser air around down, the balloon gets pushed up. Similarly, when the car accelerates, the air around gets drawn to the back of the car, which makes the helium balloon go forward.

You are shown two cylinders – one of them is made of gold and hollow, the other one is made of alloy and solid. Both of them have the same weight, shape, and are colored in black. How can you figure out which cylinder is the golden one, without scratching the paint?

Simply roll the two cylinders on the ground. The hollow one will roll farther than the solid one since it will have a higher moment of inertia.

You are in a room with nothing else but two indistinguishable iron rods. You know that one of them is magnetized, how can you figure out which one?

Touch the middle of the first rod with the end of the second rod. If the two rods get attracted to each other, then the second one is the magnet. If not, then the first one is the magnet.

Imagine you get shrunk 100 times (preserving your density), then thrown in a blender. You have 2 minutes until the blades of the blender start spinning. How are you going to escape?

If you get shrunk 100 times, but your density remains the same, your muscles will become so strong relative to your size, that you will be able to jump out of the blender. The reason is that your weight will decrease 1000000 times, but your muscle cross-section just 10000 times.

You have a jar filled with water and a glass. If you pour some water into the glass and place a cork in it, the cork will float towards the edges of the glass. What is the easiest way to make the cork float towards the center?

Since the liquid molecules adhere to the glass molecules on the sides of the glass, the water level there is higher and buoyancy makes the cork float in that direction. If you fill the glass all the way to the edge, then the water surface will be convex and the cork will float towards the center.