1) If i wanted to make a circuit with a sensor that knows when any
kind of metallic object is nearby, which kind of sensor would i have
to use ?
You need to use a metal detector to detect a metallic object i.e. an object that can pass current or modify a magnetic field it comes into vicinity of. A metal detector generates an alternating magnetic field which will induce eddy currents into a metallic object. These eddy currents remove energy from the magnetic field and this is detectable. Non conducting materials like ferrite are also detectable because of the permeability of the material modifies the applied magnetic field in a different way to induced eddy currents. Metal detectors.
2) What kind of sensor do supermarkets use?
If you are talking about shop products that have a tag read this. These generally use a 13.56MHz magnetic field and operate very similarly to a metal detector.
3) how can i increase the detection distance of such sensors?
This can be done on metal detectors by spacing the transmit and receive coils out further and piling more electrical energy into the transmit coil. On RFID tags it's harder because the tag (the portable part) has to modify the imposed magnetic field in order to make itself detectable and with a larger incident field and coils further apart it rapidly becomes a really difficult job just to double the distance. Mag field reduces as a cube law so doubling the distance means 8 times less incident field and 8 times less received signal coming back. Net effect is a reduction in received signal relative to the incident signal of 64 : 1 (simplified math alert!). That's a big deal!!
4) how could i detect (for example) a car passing by the street with
my sensor ?
Most car sensors are buried in the road and pretty much operate on the principles of metal detection.