If an airplane with two propellers has both propellers with the same rotation direction (say, both the propellers rotate counter-clockwise as seen from nose to the tail), will be the four left-turning tendencies still be generated?
Yes, for the most part.
Definitely P-factor will still exist and provide a yaw torque in the expected direction. This is why twin-engined aircraft have a "critical engine".
Engine torque will still produce a roll torque in the expected direction.
Gyroscopic precession will still produce a yaw torque in the expected direction when the aircraft pitches.
The yaw torque from the spiralling slipsteam interacting with the vertical fin-- which is normally quite significant in conventional single-engine aircraft-- is the one effect that may be be greatly reduced in a twin-engine airplane of the usual configuration, since the fin is not located in a strong part of the circulation behind either prop.
No, because they turn on different axis which does not coincide with the longitudinal axis of the airplane. Having two propellers turning the same way on the same axis, it would enforce the effect.