The idle speed does not change when the brake is applied in park or neutral.I gradually increased (by one quarter each time) the idle speed one whole turn. The vibration decreased somewhat but still there and the car feels that it won't stall when I stop at intersections.
The only drawback about this change is when I shift from Park to Reverse, the car shifts very abruptly. When I shift from Neutral to Reverse, the car shifts normally. For the time being, I plan to start the car in Neutral then shift in Reverse.
I am beginning to believe that the vibration problem may be with the connection between the engine and transmission or the transmission itself.