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.
check fluid in tranie....and LUCAS tranie lube
car will jerk forward and then go in reverse
I had a similar problem where it would shift into reverse or drive but not go immediately. Or sometimes it would drop out of gear and you'd have to rev up to get it to fall back into gear. i replaced the transmission filter and it fixed the problem.
are you pressing the brake as you try to shift?
does it shift into reverse and wont drive? if so its your tranny it needs to be replaced
Generally shifting from reverse to drive, while still rolling, is possible but not recommended. This places a lot of stress on the transmission and other components of the drive train.
Park, reverse, neutral, Drive and low
Absolutely not.
Not sure of the question, but if your car is less than 7 yrs old, apply the brake first, then you can move the shift selector.
Sounds like a torque converter lock up solenoid.
Shift linkage broken or misadjusted?
sounds like the auto transmission has a fault