I've never done a Transatlantic, despite my wife really wanting to. We've just never had the time to do it. I'm kind of jealous. The pricing looks pretty great, too.
So having admitted that, here's my two cents:
1) You have 6 consecutive sea days. This is similar to what we did when we sailed from San Francisco to Hawaii. My wife loves the sea days. She loves just relaxing, finding a spot to read, etc. We were on Princess and they were pretty good about having activities for the sea days. I would bet a lot of money that DCL will be even better about having great activities available all through the day to keep people from being bored. I would also bet that they have special stage shows that they don't show on normal itineraries. When we did 12 nights in the Med with DCL or 10 nights in the Baltic, the Walt Disney Theater had several shows that aren't in the normal rotation. Some of them were great, and to be honest, a few were stinkers (did anybody else see the "Bumblesquat Family Reunion"? ). But the point is that they went way out of their way to provide unique entertainment for the longer itinerary.
Plus, after your sea days, you have some really interesting ports of call: Ponta Delgada, Lisbon, Cadiz, Malaga, Cartagena. I would love to see Lisbon and Cadiz. Maybe take in a soccer game in Malaga.
2) It's always warm enough to swim. The pools are heated to 82°F. The AquaDunk might be chilly, tho!
3) Atlantic crossings are always liable to have rough seas, although I think in May, it shouldn't be as bad. If you were going in March or April, I'd say you were guaranteed to hit really rough seas at some point. But in mid-May, I think it's possible that you might get lucky and avoid any bad patches. (No guarantee is stated or implied!) And if you are prone to sea sickness, my daughter has always good success with Bonine (over the counter) in mitigating any nausea.
Something else to consider is that being at sea that long is likely to give you land sickness once you get off the ship. It's not usually a huge deal, but you'll feel like the entire world is rocking for a few days to a week. It usually doesn't hinder people at all (flying or driving tends to make the symptoms go away) but if you're like me you might want to plan for some extra R&R on the other side until your body adjusts.