Is the separation distance between two aircraft approaching an airport the same under CDA and Non-CDA scenario?
Continuous descent operations do not warrant a change in separation minima. The same separation minima (wake turbulence, radar minima, lateral, horizontal and vertical minima) apply at CDA airports as they do at all other airports.

To answer 2, 4 and 5 at the same time: continuous descent approach means that an aicraft descending from cruise level (typically 10-11 km.) to the final approach procedure (typically about 1000 metres) will do so in one continuous motion - e.g. without levelling out and maintaining a certain intermediate level along the way.
Although it is possible, and widely utilised, crews are not required to use idle engine thrust for the descend. It may well be the case that an aircraft is required by air traffic control to maintain a certain speed during descend, in order to establish and maintain the separation requirements mentioned above. As such, you can see CDA operations where aircraft apply thrust during descend, but where the descend is still conducted as one continuous motion.
On the final approach, usually starting at an altitude of about 1000 metres, 20 or-so km. from the airport, there is no difference between CDA and non-CDA operations. Aircraft will fly completely normally, using engine thrust and lift augmentation devices (flaps, slats) to maintain an appropriate airspeed (actually, angle of attack) so that the aircraft descends at the correct rate to hit the runway. For a normal jet aircraft, it is not possible to fly the final 20-or-so km. of the approach with idle thrust - it simply wouldn't make it to the runway.

When talking about track miles, I will assume you are talking about the distane from the top of descend (TOD) until the runway threshold (THR). For an average jet airlines, descending from a level of 10-11 km., it will take somewhere between 100 and 120 nautical miles of distance to get from TOD to runway THR. For non-CDA airports, this distance will generally be longer, because the descend has to be initiated sooner, but you will also find examples where there is almost no difference.