Figjam coolers use 1 to 2 Amps at 12V, depending on the power of your fan and pump, so figure out how many hours you want to run them. e.g. 3 hours/day * 2 coolers * 2 amps = 12 Amp-hours per day.
Those lights won't work on a 12V battery (3AA's = 4.5V, what they're designed for), so no you cannot easily hook them up cut and splice like. If you want to power lights from the battery, you can buy ordinary plug-in Christmas lights and get a power inverter. But I think having individual AA-powered strings is not so bad. Plug-in xmas lights pull about 3 to 5W per big 20ft strand, which is 0.4A, so for 8 hours of light you need 3.2 Amp-hours per night per 20ft string. And your battery is already pretty committed to the coolers.
A 5W solar panel for a 12V battery replenishes 0.4Ah per hour of sunlight at peak, maybe you'll get 2 or 3 Ah per day back.
2 coolers + 2 plug-in lights = 19 Ah/day -- a 100Ah battery will last max 5 days, but you should only run it for 3 or 4 days, the battery is not designed to be depleted fully.
2 coolers + 2 plug-in lights + panel = 16 Ah/day -- might stretch all week
2 coolers only (AA-powered lights) = 12 Ah/day -- should definitely stretch all week, don't need the panel.
To charge your iphone, you can get a power inverter and connect to the big battery (pretty negligible power required to charge a phone)... or buy a solar panel that has a USB output, like this one (note, no experience with these products, just know they exist.) http://www.amazon.com/Sunforce-22007-Co ... harger+usb