I'm sure you've seen the Verizon page specific to South Korea where you can view coverage maps and determine whether your MiFi is compatible with the South Korean network, but just in case here's the link
Calling From South Korea
You won't have any trouble with WiFi in the hotel lobby - though, without knowing details of the hotel, it's difficult to know if you'll be charged.
The iPad does not support wired-Ethernet, so you'll not be able to take advantage of that in your room.
Your iPad charger will work just fine in South Korea (and in any other country in the world too)
Enjoy your visit - it's a very beautiful country with wonderful people so I'm sure you'll enjoy your time there.
Tim
Scotland