Welcome to the boards - you're in the right place for information

I'll start with the things I know (or found) and I'm sure others will fill in the rest.
Looking
here shows us that on April the 9th 2004 the sun rose at 07:05 and set at 19:47 with high temperature of 85 degrees. Nice time to go! Of course you can't guarantee weather but the sun rise/set times should be pretty much the same year in, year out.
Discovery Cove This really is an all day thing. You have to book well in advance and its not cheap as they only allow a set number of vistors in on any given day, I think the max is around 1000. Last time we went it would've cost >£500 for a single day in DC for 6 of us and although we would have liked to have done it, we couldn't justify the cost. So if you are going to do DC you really must make a full day out of the experience!
Disney Parks, more than one in a day? Well, not really. The parks are so big, varied and spread out that you'd miss so much and that would be such a shame. Depending on the tickets you buy for Disney, either the Hopper or the new 'Own Way' versions, you can move between parks on the same day. However, to do each park justice you really have to give it a full day there, in all honesty, it would be difficult to do everything each park has to offer in two full days. Personally, what we tend to do is have a full day at a park and then use the 'hopping' facility to cross into another park for the late parades/firework shows. For example, spend all day at Animal Kingdom and then hop to one of the others for the late shows at Magic Kingdom, EPCOT or MGM. You might also be able to catch a couple of rides before the firework shows begin. Use the park hopping facility where you can but make the most of your full days at the Disney parks, you'll need them!
About the best information I could find on mosquitoes was
here. (I love Google!) It doesn't tell us the season but it says their not breeding well at the moment!
Supermarkets. Last time we were there we used a couple of Publix supermarkets on the 192 and Highway 27, both of these closed (if memory serves me correctly) at 22:00. No doubt there are some 24 hour supermarkets (especially in the Kissemme area), hopefully someone who's stayed there will be able to confirm this.
I hope these replies are usefull and that others can fill in the blanks and/or correct my mistakes! I really can recommend a copy of Simon V's excellent book
A Brits Guide To Orlando as this is a veritable gold mine of information to help you plan your trip.
Good luck - and have fun!