To be absolutely sure, I would check with the embassy. But I believe a confirmation of your PR like COPR and any/all documents that you received when you did your landing procedures will be sufficient.
The again, call the US embassy directly to be sure.
Bear in mind, you won't be able to fly back to Canada without your PR card.
So if you are planning on flying, you'll need a PRTD... or to plan your trip as to cross back at a land crossing where you don't require but would advise you take your CoPR.
Early April? Should really have it by now, I'll call and find our what's happening, it could be in the post.
Yes you can, absolutely. Be sure to carry your COPR for proof of PR and proof of funds to cover your expenses.
You may need to provide these, but not necessarily.
As mentioned by one poster, give thought to your return - without a PR card you can't travel back to Canada on any commercial transport system - air, train, bus or boat. You can only re-enter by road, using a private vehicle.