Try not shifting until the car is no longer accelerating. That is, let it reach a constant speed in first gear before you depress the clutch. That should eliminate any "slippage on the flywheel" when it is disengaged. There are springs in the clutch disk that are designed to give a little to provide a smoother action but they usually are just used when engaging the clutch. Because of the low gearing in first and reverse there would be some bearings in the tranny that would be spinning more when in the lower gears. You may be hearing that noise although you shouldn't unless: 1) the bearing is wearing out, 2) the tranny has low lubricant or 3) maybe a tranny mount is bad and it is resting on a frame member and just transferring sound to the car body.