Engine does not idle fast when cold and is hard to get going without killing engine. Sometimes idel is as fast as 1500 RPM when warm, but mostly is OK when warm.

There are 2 idle specs. One is in gear with brake applied. What is that speed?

to fast hot and too fast cold that it?
well here is normal, its a G16 engine, a Vitara with Sidekick badge.
G16 in cold weather, start and race idle at about 1500 rpm
or more if in ALASKA, you never said that or how cold it is.
the IAC valve is thermal, it and opens more colder, a fact.
the 8valve engine (black steel top) is faster. cold idle
then drops in a few seconds, to 1500rpm
at this time, the ECU brain does NOT control idle speeds at all.
the the engine warms up by virtue of the thermostat
as it warms to 150F to on way to 180f stock temp.
the ECU then takes control of the idle speeds.
got that so far?
so at 180f the idle is 800 rpm (800 is hard coded in the ECU,
ad ECU regulates this, unless you turn on the A.C , and if that happens 1000rpm is called up.
if not the ECU cant control it or the ECU is in limphome mode or worse.

if you insert the diagnostic jumper
does the CEL lamp flash 12s
it must.
see this paper clip this is your only scan tool.
it is crude but that is all you get until 1996.

http://www.fixkick.com/CEL/CEL.html#OBD1codes

YES, 750 to 850 rpm after warm up.

Most engines always fast idle to warm up.

I've seen from 500 to 1500 RPM in all the manuals I've been through, depending on the year and application (truck/car). In personal experience, 650-800 RPM is acceptable warm operation range. This will also depend on elevation. Will go up to 1200-1500 RPM for cold starting. I live at about 2000ft and my '86 Pickup 22RE idles at 725-750 like a top after about a 3-4 min warm up @ 1250 RPM if it's cold (<45ish).

That would be your engine "choke" functioning. It's not a problem. The choke engages when engine is cold and shoots extra fuel to the cylinders to idle the engine up especially in cold with. Once the engine has sufficiently warmed up, the engine will idle back down.

The choke cam, which advances idling when the engine is cold, is possibly stuck in a partially closed position. A spray of penetrant oil with a bit of manipulation of the shaft should fix that problem.

Sounds like you have a vacume leak on your brake booster ....with engine running have someone press the brake while you listen on the driver side by the master cylinder the large vacume line going to the booster behind the master cylinder is most likely the vacume leak...and if so you can get what you need at your local parts store ...

please change the idling switch control valve assembly plus the sensor!

could be a vacume leak. check hose for cracks or lose conections.