Adding 2" PVC sanitary T to 3" copper drain pipe

[David Criss]

The last room of this house is a half bath; toilet and sink. There is a 3" copper waste pipe under the floor that T's up to a toilet, then continues under the floor and does a right angle up the wall through the roof and becomes the vent stack. About 15" up from the floor there is an 1-1/4" stub out for a sink drain.

They want a front loader washer and dryer in this room and to move the sink into the corner. My intention is to cut the 3" copper and add a 2" PVC to pick up the washer and a 1-1/2" PVC to pick up the sink.

I've no idea how to add PVC to 3" copper pipe.
Do I need more vent for the washer? I could add a quick vent.

Thanks, David