Could be several reasons but a vacuum leak would be most likely.
Vacuum leek
the choke is on
did you find a solution yet
The cause of high engine idle and surges in the 1989 Corvette is due to..Read More
a/c kicks on
Either your fuel is burning too rich or you have an idle censor out. new idle censor's are not expensive
Check throttle positioning sensor.
A sticking choke or vacuum leak are two common causes.
Could be a vacuum leak
My Knowledge is temp. coolant sensor the small one.
I would look for a vacuum leak.
The increased idle when started is normal, all properly working cars that aren't ancient will do it. As far as the hard shift goes, your tranny.