Hi raider,
By door thingies, I guess you mean the roll up door panels at the hanger deck openings. If so, you can leave some off as though they were rolled up, sure.
The Essex, like most CVs of the class had at least two paint schemes during the war. The ships went through lots of rapid changes as radar and communication gear improvements were happening very fast. Antenna locations, mast changes, etc., varied widely. So you have to nail down a specific time segment and build toward it.
Easiest scheme, of course, is the Navy Blue measure 21 scheme. All vertical surfaces are 5N Navy Blue all horizontal surfaces are 20B Deck Blue. The flight deck was stained to match. This site is a big help http://www.shipcamouflage.com/measures.htm
When I've done my carriers, I've airbrushed the basic hull and island. Detail parts I paint with a brush, depending on whether I can use plastic cement or if I need super glue for PE stuff. Since I tend to weather the model, some of the base coat doesn't matter all that much. I've never done a dazzle scheme in 1/700. Sure somebody will chime in for that.
Have fun with it.
Mike