Moving Laundry Room

In an effort to expand my new kitchen I am forced to move the laundry to my garage and make a new room there.
Here are my questions:
can I drill into the studs to run drain line horozontally and vertical for vent. ( the walls are exterior hose walls but interior for the garage, if that makes sense.). I am concerned about them being supporting walls.
can I connect the vent to existing vent pipe in the attic and remove the old vent below where the washer was. ( it is about a 12 foot run, this would avoid cutting a new hole in my roof until a later date.)
what size dryer vent will fit in a 2x4 wall cavity and can I run it through the header into the attic.

Thanks for any help.

You can connect the drain vent in the attic. The run should have slope so if any moisture gets in, say from rain, it can drain instead of pooling somewhere. You can buy round to oval duct pieces and run the stuff in the wall, but I'd be worried about the lower velocity maybe collecting lint in the bottom. Hope you are planning to exhaust it to the outside and not into the attic...a very bad idea.

While the drain line should be 2", you could probably get by with a 1.5" vent line (wait for the pros), if so, then you can run that through studs.

Jim, thank you for the reply. Sorry for not getting back sooner.
So I should be able to run the 2" drain through the studs and down to the basement through the floor plate and the 1.5" vent through the top plate into the attic.
What about the dryer vent?
Also the current plumbing is copper, how do I cut into the copper and use pvc pipe for the drains and vent.

You can convert the copper to PVC by using a male copper threaded adapter and then a matching female threaded PVC fitting. Be forewarned - copper fitting prices have gone up a bit - I paid nearly $10 for a 1.5" one a few weeks ago.

You can cut the copper with a pipe cutter or sawzall with a metal blade. If you use the latter be sure to go slow and cut it clean. File off any burrs and clean the fittings well before soldering.