1) Yes, Delta can check your bags all the way through, as MU is a partner where they do this, even on two different tickets. If the check-in agent in DTW gives you a hard time, push back and have them look it up. I had this issue in ATL earlier this year, and they looked it up. No issue once they did.

2) It's been my experience that the operating carrier must check you in, not who you booked the flight through. So you'd need to check-in with MU. PVG has free Wi-Fi in the arrivals area near immigration. I don't remember seeing a transfer desk at all prior to immigration; but I didn't need it, so I wasn't looking for it.

3) Try MU online check-in? Never done it. Always checked in at the airport when I've flown MU.

4) Transit for I-I, when I did MU-MU wasn't bad, pretty painless. I can't imagine DL-MU would be different as DL parks their jets at the same terminal as the other MU jets. It's really a beautiful sight seeing DL jets over there. Anyway, you'll walk down this long hallway. Go to the automated kiosk, scan your passport and fingers. Take a left in the arrivals hall, as you don't want to go through immigration. You'll use automated gates. Scan your passport and boarding pass and then go on to security. Look for the VIP line as you're a Skyteam Elite+. Just act as if you're supposed to be there and you'll be fine. Not once did anyone ask to check my boarding pass when I went to those lines; the lines don't explicitly say Skyteam Priority. Then you're in the international terminal. Not a painful process at all. Though the terminal is boring AF. The lounge isn't bad, but there's no view at all. Second floor is AC'd quite nicely, and is quiet. Agents there all speak English well, or they'll find someone who speaks well.

Maybe I've just been really lucky this year as I've yet to have an issue at PVG. I guess the MU flights to/from JFK are at off peak hours?