Welcome and congratulation
s! I just adopted my Pyr from rescue this past October and had some of the exact same issues for the first couple of weeks or so. Jenny didn't eat much at all for a while, I think it was due in part to the stress but also getting used to a higher quality food. She eats just fine now.
When I first got her it seemed to me that she never went pee! I would take her outside to go and she just wouldn't!! But as I continued to take her out at regular times of the day, she seemed to learn that that's when it's time to go and she is much more regular about peeing these days. I use a retractable leash with her when I take her out.
Jenny pawed also and I have 4 yr old twins and it hurts too much when a big dog does this, so what worked for us was to turn our backs and completely ignore her when she pawed and then as soon as she put that paw back on the floor, we lavished her with treats and love. She caught on very quickly and after a couple of days she didn't paw us anymore.
Your guy sounds like a real sweetheart and I'm sure you'll enjoy this site. I have learned so much and love this breed. BTW, you definitely can't let a Pyr be outside in an unfenced area off-leash. The saying goes, "What do you call a Pyr off leash? A disa-pyr!"