I'm surprised your travel agent didn't provide this information to you much sooner than this, but hopefully people here will be of help to you.
First, as for shore excursions, I understand your feelings about booking with the ship, but trust me when I say that using one of the major independent companies, such as Shore Trips, is a much better way to go. We've not only used them personally on many occasions, but have literally had thousands booked by our clients and no one has ever had any problems whatsoever. I would much rather use them than Carnival any day for many reasons!
As for when to get to the pier, boarding will normally start around noon. However, people will start getting in line a couple of hours before that, so the initial line is very long. Plus, they won't let you into your cabin until around 1:30, so even if you do get onboard earlier, you're going to be waiting at the buffet on the Lido Deck with everyone else while they lug around their carry on suitcases. Keep in mind that you do have to be at the pier by 2:30 because the ship leaves at 4:00 and TSA requires the cruise line to submit their final passenger manifest 60 minutes prior to sailing. So, the cruise line would like you to be there 30 minutes prior to that just to make sure you complete your check-in in time to get on the ship. Personally, we like to arrive around 2:00 - 2:30 because there are no lines, cabins have been opened, and it just makes it alot less hassle. We don't like lines and we hate waiting. If we're staying at a local hotel, we'll request a late check-out, have a good night's sleep and get up late, take our time having a relaxing breakfast, and leisurely make our way to the ship. Makes it so much nicer and much more relaxing as we don't feel rushed.
As for carry-on, I always suggest taking a backpack or small suitcase as you want to keep all of your electronics (cameras, computers, etc.) with you as well as all medications. Plus, it'll be a while (usually a few hours) before you see your suitcases, so you might also want to take some toiletries in case you'd like to freshen up in your room. (You could wait in line in a hot sweaty environment and wish to take a shower and change clothes.) Plus, the backpack/suitcase can be used the morning of disembarkation to carry your nightclothes, toiletries, and electronics off the ship.
Hope this helps.