Penny gave you great answers but left some holes that I will attempt to fill for you.
Camp carnival- They will tend to let the old children drop an age group if there are close but not vice versa. They have every right to be strict with this, but we have had good luck going on the first day to the camp carnival "welcome aboard" Q&A and sign up session they have and asking the CC person in charge of that group answer if she would be willing to have the older child in with the younger one. It is really up to her. Now realize that it has been 4 or five years since we have needed to do this but it is worth asking.
Internet usage- Gosh no, don't attempt to upload your photos to your website storage, the fees would be out of this world! You can get minute packages for internet usage but we are talking like $100 for an hour worth of access. AND that access is very slow compared to being at home. It really is only good for email and light web usage. To upload the data for pictures would burn up minutes very quickly, not to mention make you spend valuable cruising time sitting in the enet cafe instead of having fun. You would be MUCH better off just buying 2 or 3 (or one really big one) memory cards for you camera. fill one up and plop in the next one. Two weeks ago I brought two 2 gig memory cards and didn't use up the first one and I took lots of pictures and videos...
Verizon- Yes, you will have Verizon service onboard but again the price is an issue. You pay international roaming rates which are I think $1.99 a minute for voice calls and 25 cents per text. I don't know for sure if the ship's service has a good data rate as I only used my phone for a couple of texts. You sure don't want to set your teenager loose with a text phone or your bill will be $1000 bucks... The cell coverage is provided by a company called Cellular at Sea... google on them and you will get more information. Verizon contacts through them to provide service. Its cheaper than paying for ship to shore phone calls but not greatly. Only use the cell phone ON THE SHIP in emergencies. Many of the islands have cell coverage. Go to the VW website and look each of them up to see what your fees would be so you know... Oh and a word to the wise.. make sure your children know NEVER to use the phone in the cabin to try to call your cell phone. Our child did this and just trying to connect twice (she got the voice mail each time because the phone was of course turned off) but for those 2 1 minute call we were charged like $40
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013