1993 Buick Century

Humming on curves between 35 and 50 mph is a front wheel bearing. It's usually the one that gets more weight, i.E, the side opposite the direction of steer, although sometimes the reverse is true. This may also be the source of the rumble and vibration, or it may be another steering or suspension component. The lunging and stalling, as your mechanic said, is probably a failed torque converter clutch solenoid, sometimes called a lock-up solenoid. As the term implies, it makes a firm connection between the engine and transmission at cruising speeds, like letting out the clutch on a manual transmission. It's not letting go when it should. It can be replaced without removing the transmission from the car.