As to choice of adhesive, there are a few ways to go, epoxy for one (look for laminating epoxy), aliphatic another, polyurethane (foams up as it cures) seems to be the new favorite. Here's one website with good photos & text: http://www.mackrc.net/patternwings2/index.htm

As to removing foam pieces from the cores before sheeting, it can be done, but is rather laborious. It also creates problems as to just where to remove and where to leave for structural integrity. It is a process best left to those willing to accept unsuccessful experiments. A lot of bother for not much weight saving, in my humble opinion.

As to weight of the finished wing, two areas to focus on are the amount of glue used and the weight of the balsa skins. Use the least amount of glue that will give good bonding from balsa to foam core. I would think aliphatic would be the lightest of the glue choices, but have yet to experiment with that myself. I like the polyurethane. Its foaming action creeps into voids, and its viscosity is thin enough that it can readily be spread out for a very thin coating. Also it has a very strong bond. Keep it off your skin (human skin). Not toxic (that I know of), but sticks good and doesn't wear off for days.

I weighed the balsa sheet pack that came with a quarter-scale kit a few days ago and calculated the wood is nearly 14 pounds per cubic foot. Contest balsa, if you can find any, would be less than half that. I figured if I used the wood in the kit, it would cost me close to two pounds in the finished weight as compared to contest balsa. That's a lot of heavy wood--more than a 10% weight penalty. Having been unsuccessful in finding any truly contest grade wood I decided to take a chance on a quantity of AAA grade balsa, which with a little luck might come out around 8-9 lbs/cu ft. We'll see when it gets here. I will sort the pieces out and use the very lightest for sheeting the tail parts, next lightest for sheeting fuselage parts aft of CG, then the rest for wings and forward fuselage.