Q: 2008 Mazda 5 has codes P0661 and P0720

I've engine fault lights up, so I went to nearby workshop to check. He used a wireless device to test and the error code is P0661. He cleared the error and I ask me to come back if error comes out again. The next day the engine fault lights up again and then goes off the next day. I ignore and continue to drive for a week. Then suddenly while on the highway, the engine fault and AT lights up, the car jerk a little then AT light goes off. But the engine fault remains on. I went to another mechanic, this time the computer they use is wired type. The error fault they found now is OSS, and I couldn't remember the code. It could be be P0720 or P0721 etc. He replaced the speed sensor. I thought the issue solved but two days later the car jerk at the highway again. The AT lights up followed by engine fault lights up. The AT light then goes off. These light keeps going on and then off again the next day or day after. What do you think the root cause can be? Could it be the Gearbox spoil?

My car has 130000 miles.
My car has an automatic transmission.