CF-40 will draw about 2amps per hour.
2 amps x 24 hours = 48 amp hours
BUT you dont want to deplete a battery past 50% max so I would suggest a 100amp hour battery.
That'll last you a day off power (though most people with a 100 AH battery and smaller fridge like you have will get 2-3 days use out of such a size).
Derek from COCIA wrote a bit up about his setup with a small battery CF-50 here : viewtopic.php?f=22&t=1807
A small solar set up such as an 80 watt folding kit should keep such a setup running without any troubles what so ever and these days they are a lot more affordable than 2+ years ago.
Derek paid about $1200 for his now you can get them for under $400 http://cgi.ebay.com.au/80W-FOLDING-SOLA ... 415270b7bc
I agree that a 3 way fridge "may" be a better option for you with the limited space.
20L steel drum sitting on the fire for a while till it heats up then a portable battery shower (you can get ones that use a 6V battery or ones that run off the cigar lighter in the car) is ideal if you want showers - but you have to have water accessable.
LED and CCFL lanterns are great and its likely that for 2-3 days you wont have to charge them (especially the LED units) But always take a gas lantern as backup.
Gas stoves. high pressure is cheapest - low pressure is more expensive, less common but WAY less prone to issues and they make your gas go further. BUT if you use a low pressure stove you will have to have a seperate gas bottle for a gas lantern because AFAIK there are no low pressure lanterns and I've not seen a way of connecting both a high pressure and a low pressure device to the one bottle. A gas fitter might be able to chime in here if such a beast exists. Theres also dual fuel stoves - personally I preffer gas.
Most national parks dont allow fires unless in designated fire pits. Most state parks are a lot more relaxed on the rules regarding fires
For the frozen block ice - you dont need / want to smash them up they work best when solid. Its a large thermal mass to transfer heat energy that way.
I've never camped on a powered site that I know of and never had an issue