We have been on the ships twice in February and didn't catch the flu. It's definitely possible; it just means wash your hands and enter the ship healthy. (the cruise lines make you sign a form saying you have not thrown up or had a fever in the last 24 hours before boarding; definitely people can lie but I let you know this because the cast members and the cruise line industry takes illness very seriously)
I have been on all four ships at this point. I found that the Fantasy and the Dream were so large that I didn't have the sensation of moving until I was off the ship at the end of the cruise.
Yes, it will be fun and relaxing. There is a full third of the ship dedicated just to adults. When we were on the Wonder, we actually had the adult pool to ourselves (and one cast member sweeping) one early evening for an hour. It felt like we were on our own yacht. You can plan your excursion to have or to not have children attend. It's not that you won't see children; its that you do have a choice of how much interaction you want to have by your decision on how to spend your time. Children won't be at tastings and there are many activities designed just for adults.
Enjoy! It really is a wonderful way to vacation.
