I'm not ENTIRELY sure on how to transfer, but I believe you have to take your original (plastic-encased) HDD out of the plastic, to insert it into the 360 S. Or, maybe a transfer cable? Also, I don't think (don't quote me on this), but I don't think the new Slims have ports for memory cards. Not sure. They do have built in wireless though!
I just got my console back on the 26th (about 15 days of waiting, 99% of it was shipping time to and fro). I sent it in for E74, though the GPU pretty much died and didn't give E74. They took it, replaced everything inside (CD drive + mobo + GPU), and gave me my same console back. It's pretty fantastic, and quieter. I haven't checked to see what parts I got back, but I had a Zephyr before.
I didn't call. I just went online, logged in, and submitted a repair request for my already-registered console. You have the option of either them mailing you a shipping label, or you can print one out, and take it to a UPS store. Good luck finding a box... I used a 14x14x14 (from Walmart, $0.64) and cut it down to about half its size. You should get some bubble wrap, too, and completely wrap it up, and stuff the box with something like newspaper or peanuts. Of course, UPS will package it for a fee, too.
All you send is the console, with its original face plate. Nothing else. No controllers, cables, memory cards, or custom faceplates.