This doesn’t happen all the time, but sometimes when parking and I put my car into Reverse, it jolts/jerks. My car drives in reverse with no problems, but using the gear shift for Reverse is when it happens. Another difficulty is when I accelerate, the car does not normally increase speed until I have reached over 30 mph. Also when in Drive it’s the only one gear that never upshifts or downshifts. I’m thinking this means my car is in limp mode. What needs to be done to repair my car?

First of all is the SES light o in the dash? If so you need to get the DTC's read and go from there. If not it might be time for a transmission fluid change. Don't do a full flush, just a drain and fill. If that doesn't fix the issue it might be time to take it to a competent mechanic.