Some sort of organic biodome would be required for sustainable resources. Food, carbon dioxide filtration, lots of uses. Would be a fun level if done right too.
As to why Brink's "island" is so hot, it is simple. Ice reflects most energy(light), while water absorbs most energy. If the ice caps are all gone, the worlds temperture will increase, and snowfall probably won't happen in the middle of the ocean(probably only on the highest peaks of land mass, if at all). Seasons will probably fade away, as the oceans conveyor system will stop working which helps balance world temperature. There isnt enough water on earth to submerge all of the land mass around the world. Also, as the water temperature rises, hurricanes will be more frequent and more powerful around the world, and occur in places they previously havent(If you live in New York, you might want to move in the next 10-20 years). These new hurricanes will make the ones we see today look like lil cute baby hurricanes. There wouldn't be a "safe place" for this island unles it was built in the far north or far south, and even that is a maybe.
There high and low areas, valleys would be flooded, the peaks will still be there. Hawaii formed in the middle of the ocean, due to high volcanic activity. It has the potential to rise with sea level with enough volcanic activity. As for Mount Everest being under water, you do relize it is ~30000 feet high right? The water level isn't going to be 6 miles higher, a most a few 1000 feet.
(In the real world) There is a reason global warming is a big issue right now, and yes I am a super nerd. We also might be on the verge of our magnetic core shifting, which no one knows what would really happen except your compas will point in opposite directions.
That being said, Brink does use some of the concepts of the real world, but I doubt the use them all, so any scenario is possible.
http://www.sciencedaily.com/releases/2008/09/080926105021.htm if you are curious abotu the magnetic core. If you can't find good science articles about real effects of global warming, shame on you.