q1 - no, this is the transmission speed sensor
q2 - not likely, but its possible the TCM (transmission control module) is fried. try disconnecting your battery for a while to clear the computer.
q3 - sounds about right to me. much more likely that the sensor is gone than the computer software. however, a reprogram is quite cheap - my dealer here quoted me $40 and if its under a TSB they should do it for free. check at
Hyundai Service Website. you need to get an account, but its free and very worthwhile. all hyundai factory manuals
q4 - no
finally, the trans getting locked in 2/3 gear is actually a failsafe. according to hmaservice.com here are your possible causes:
● Signal circuit is open or short.
● Sensor power circuit is open
● Sensor ground circuit is open
● Faulty OUTPUT SPEED SENSOR
● Faulty PCM/TCM
given the year of the car, i'd say its far more likely to have a bad sensor than to have bad wiring or a bad TCM. again, check your TSB's and see if that helps. quote the TSB # when you visit a dealer.
hope that helps.