We bought a zip up nylon carrier for Barney when he was a puppy. I would put it beside me in the bed and when he would whine, I would put my hand up beside the mesh. This really helped him to sleep through the night. When he was big enough that I wasn't worried about him falling off the bed, I quit using it. I got a cheap Wal-Mart bag similar to this one.
Amazon
As far as the pooping goes, are you sure he isn't eating it? Sometimes they do this. He's very young to have him outside. I wouldn't do this until he's fully vaccinated. I would put him in a play pen during the day time hours and put his food and play stuff on one side and potty pads on the other. I took Barney outside when he was about that age and he got giardia. It took forever for him to get over it.
http://www.amazon.com/IRIS-Indoor-Outdoor-Plastic-...
Congrats on your new puppy and welcome to YT. I can't wait to hear all the fun stories about your cute new baby.