Is it possible to use the track instead of headings in the aim to apply a radar separation?
Radar controllers take wind into consideration when issuing headings - "Fly heading one six zero".
Issuing a track would not be practical. This puts the burden of figuring out what course to fly on the pilot. Not all aircraft have a glass cockpit or instrumentation necessary to easily, quickly, and accurately compute a heading to fly to stay on course. The radar controller knows real-time information, knows the 'big picture', and has practice issuing headings.
Actual position is used to provide separation. Heading doesn't matter for separation.
No, ATC will not issue instructions to aircraft to maintain a specific track. From ICAO Document 4444 (PANS-ATM):
188.8.131.52 Vectoring shall be achieved by issuing to the pilot specific headings which will enable the aircraft to maintain the desired track.
If a controller wishes an aircraft to fly a specific track toward/away from a VOR navigational beacon, they may instruct pilots to fly a certain VOR radial, which is essentially a track. However, this only works if flying to or from a VOR or similar beacon.