Hi.

Which light weight flexible core material(nomex, 3d core pet, soric, etc) would you recommend(3-5mm) for ooa low temperature prepreg part(light weight monocoque)? I plan to use 2/2 twill 3K carbonan for outer layers + 6K inner layer and a core inside.
Would the core material require any adhesives or is it as simple as laying it on top of inner layer and proceed with second inner layer, outer layer then bagging and vacuum curing the whole thing at 1 shot? 

I have built 65 small sailing boat hulls like the one in my avatar that are pre preg and PVC foam core with no film glues. Never had any problems come back at me.
These were mostly 1 x 200g carbon, 100kg PVC core (herex and divinycell), 1 x 200g carbon on the inner skin. Then also local areas of extra layers for reinforcing.
I would firstly heat form the foam in the moulds under vacuum at 100 degreesC. Then remove from the moulds.
Outer skin layers first in the mould and then vacuum the foam pieces in the moulds as below.
Then inner skin layers, vacuum and cook.
I my case the hulls do not have a perfect surface finish (they have an even weave porosity all over) but hand work with filling and primers fixes all this. My own peel tests seem quite good still.
I am quite sure that having a fine surface foam such as 100kg density or better helps (some 80kg are very open surface cells). Also note that vacuum forming the foam directly to the moulds first also smooths the foam surface with the heat/softening and pressure so there is no excessive open cell surface to take too much resin away from the carbon.