A local locksmith should be able to re-key or replace the existing lock cylinders. I would probably leave the existing hasps on there for insurance while towing, not necessarily to protect the contents from theft but rather to prevent the doors from flying open if the walls flex enough to let the door escape from the factory striker plate. (My trailer dealer warned me to use the deadbolt on my trailer's side door when towing for this reason, and it is probably why most cargo and truck trailers come with cam-lock bars on the doors.)
To get the doors to open from inside. I would suggest retrofitting an RV door handle and lock onto the side door. Here is a web page showing several different styles:
http://www.rvdiscountsuppliers.com/rv-parts-hardware-entrance-door-hatch-locks.htm
If you're lucky, one of those handles will bolt right in as a replacement for the existing handles. Shop the price, because I only linked to this particular web site because they showed the various options on one page.
There are plenty of pictures here of people installing pink or blue foam insulation sheets from the DIY home improvement stores. I will let someone else address vapor barriers and problems with condensation on interior wall screws if you decide to cover the insulation.
My suggestion from working with two different volunteer clubs and their equipment trailers is to get your core members together at someone's house on a weekend and pretend that you're setting up for an event. Once everything is set up, tear it down and pack up. As a group, figure out how to best make the trailer functional for both hauling equipment and as a mobile office at your events. The only design constraint is to make sure that you have about 10% of the trailer's total weight on the tongue when loaded, or else it will sway all over the road.
I have no idea what is involved with your events, but running autocross events in parking lots and airports requires us to transport 200+ traffic cones. We need to run a registration table in the morning, and then timing/scoring during the driving event. Our recent useful lifetime out of a 10' x 10' EZ-Up canopy is two events due to wind damage, and trying to operate computers in the rain or bright sun without a tent is really a challenge. One of the two clubs that I'm active in purchased a concession trailer with a flip-up side window, which allows us to run registration and timing/scoring from inside. The other club is already on their second EZ-Up of 2011, and is looking into a concession trailer or possibly a concession truck with air conditioning.
If you take a look at the photo galleries and postings of some participants here, you will come up with some great ideas for optimizing your trailer. In the past month or so, someone posted pictures hanging Suncast plastic garage cabinets in their trailer for storage. I am already sizing up the entire Suncast collection for my own race car hauler, since they probably weigh less than custom metal trailer cabinets and cost 1/4 the price. I saw someone a few days ago posted a picture of an over-the-door canvas shoe holder being used inside a trailer to hold loose cans and things, which I thought was another brilliant idea. I don't think that anyone here is a professional trailer builder, so everything including installing doors and windows that you see being done has been performed DIY by people who have never done it before. If you have any other questions, feel free to ask.....