Yes I have repaired such issues with honda city CVT unit - the electrohydraulic unit on top of it needed some working. But there was a 50% chance of failure, - I'll explain you in simple way, the variator (cone assembly) moves in and out, it does this via grooves in the center shaft part and ball bearings in the grooves to keep it aligned, if those grooves are worn down and the ball bearings are siezing then the unit will feel like its dragging - in Honda the starting clutch deapplies and the car remains stationary when it stops, in the toyota units the torque converter has no input at idle speed, both face the same jerk start behaviour once power is applied.
anyway - I would suggest you get a zero calibration done, this calibration is for the "acceleration" sensor in the air bag module - you might ask why airbag module - the ECU needs to see instant change of acceleration compared to the ground as input translating to vehicular motion (very useful on downhill and uphill)
If this calibration is messed up the transmission will not coast at the right time and you will get a draggy feeling.
the wheel heat up is a simple job for any sensible mechanic, just make sure to find some silicone grease to lube the pins, dont use "parts ki dukaan ki grease dibbi" on brakes.
