I don't have the answers to all your questions but I will try.
1. Sure is. I think the kids will love it. But be prepared for the crowds on the weekend.
2. Not sure where to get discount tickets.
3. Perhaps the Lotte Hotel located just adjacent to the park would be an option? You could save a lot of time commuting to and from. Perhaps they give you a discount to Lotte World for staying at the hotel?
4. Take the Limo Bus from the airport direct to the hotel. You can find more infor
here.