From what I saw, losing just once per stage unlocks the full progression of cg for that stage in gallery although ingame it takes 3 losses to see the full progression. One loss is also enough to trigger after-mission event at base that will progress each stage that will accumulate and progress for each new stage you died at least once in.
The double xp most likely refers to when you have the humiliated status. If a character hits 0 hp from rape but you win the battle, she revives with 1 hp with a humiliated status unique to that stage. Alternatively if you party wipe I believe your whole party also gets the status unique to that stage. The status can be cleared by the short haired girl's 100 tp support skill that repairs armor. Stage 1 is body writing, 2 is tentacle suit, 3 is big belly, 4 is mind / modified battle suit, 5 is bondage, each one has unique penalties though i only noticed 4 + 5 to be noticeably problematic. Note a stage can contain enemies from prior stage which can land the earlier status on you via rape to 0 hp, eg. you can get tentacle suit status in stage 5 for example, this is probably useful for 2x exp without getting tagged by a dangerous status like stage 4+5.
I do much prefer to fight naked (scientist in stage 1 / 3 / 5 sells a free armor remover along with suicide poison) since that enhances attack power at the cost of defense.
Honestly though game is extremely easy, you can blow thru everything without worrying about 2x exp at all. I went thru it wiping every enemy on every stage and the perma stat upgrade are cheap and powerful, I ended up only using money from stage 1-3 on only attacking power, a little bit of hp and mp and blew thru everything w no challenge.