At idle, RPM should stay stable, though it may increase a bit with AC turned on but still it should be stable (around 800).
2) While downshifting gears i-e from 3rd to second or second to first the rpms drop to 600, and occasionally to 400.Is this normal?
It all depends on the RPM of your engine,
Say if you were at 80km/h and you downshifted to 2nd from 3rd then RPM might show 6k but if you do the same with speed at 60kmh then the RPM may show 4k (If RPM meter is working properly).
3) Should the rpms drop below 600 while having second gear at low speeds?
Yes not only in second gear, but in every gear.
Each gear has its upper limits and lower limits,
If you drive the car at lower limit of any gear the RPM will drop and if you further drop below the lower limits of any gear than the car will stop.