Hey guys I'm wondering if this is a common issue with the BB6

When I start up the car and put it from Park to gear D4, theres a awkward vibration that comes up for 2-4 seconds after I roll (with a tiny bit of gas) about 20-30/60-80 ft away from any parked area. Its like vibrating from under the driver side seat and feels like its coming from the front of the car. At first, I thought it was maybe the abs system that comes on? since this only happens when i first start the car and pull out of a spot. If i were to stop the car, put it into park, and then into gear again, the vibration would never come up so it only happens during the initial start up.

As for other things I've noticed, the Prelude has these weird shifts from 1->2 that feels like it catches late at 2.8rpm and then chugs the whole car before moving after a complete stop. Its getting to a point where i have to use SS just to move forward smoothly. Its a 2001 with a little over 65k on the motor and trans plus the car is just my daily so I'm not driving it hard at all. If it boils down to it I'm willing to get a 5 speed swap if the trans is going out but I rather just keep it as it is and build another E36/2.5RS down the road...

Any suggestions or info would be greatly appreciated. Thanks in advance!