Is "Flight Idle" for a jet engine a constant N1% value or does it vary with Altitude, and OAT?
This will vary from engine to engine and with modern engines controlled by computers for max fuel efficiency, the computer will constantly adjust the idle during the descent unless you manually select otherwise. However a minimum idle speed is necessary to prevent flame-out, and is as high as 70%** during severe icing conditions although 55% is the minimum. There are also different idle regimes, flight idle, approach idle and ground idle, controlled automatically.
The last aircraft that I flew, the B727, did not have any fancy FADEC and we manually closed the throttles at top of descent. The fuel control unit would adjust the fuel flow throughout the descent to keep a minimum 55% N1. This was evident from observing the fuel flow increase throughout the descent even though the throttles were at idle. If we needed more N1 due to icing, we would have to advance the throttles manually. Some planes had autothrottle but I don't think it compensated for icing.
Approach idle is also controlled automatically and is somewhat higher to allow a quick spool-up in the event of a go-around. It is deactivated after touchdown.
The 737Ng has similar regimes controlled by the EEC (Electronic Engine Control).
** Thrust requirements for for engine and wing anti-ice:
If Icing conditions exist with TAT -7° or above: 55% N1
If Icing conditions exist with TAT below -7° or moderate to severe icing observed at any temperature: 70% N1
Only one outboard engine supplying bleed air for wing 75% N1 on that engine.
To answer your question below, a jet engine works much the same as a piston engine wrt air/fuel ratio and the compression ratio is determined by its construction (see NASA). In a jet engine however you don't have a butterfly valve to vary air input, you can only vary fuel input-(there are exceptions with bleed-off valves, but let's keep it simple). The speed at which the engine turns determines air input and this speed is regulated by the amount of fuel injected into the combustion chamber. The jet engine will automatically settle at an equilibrium speed when the best air/fuel ratio is achieved.
So assuming an engine with only a variable fuel input (no automatic compensation for any variable parameters such as altitude)--- if for instance the altitude at start of descent is higher, less air is going to be taken in by the compressor, the fuel/air ratio will change resulting in a different engine speed than if the start of descent altitude was lower.
Ram air effect (Indicated airspeed) will also change the fuel/air ratio once again causing a different equilibrium engine speed.
Temperature will also affect the density of the air and cause a different rotation speed.
This is clearly unacceptable therefore some kind of governor must be provided to maintain stable parameters.
You can use the NASA engine simulator here to play around and test various scenarios.