Male bonding. And it is ridiculously common in Japan where there are communal baths. Heck, there are even some places iirc that are mixed baths.
As to Nakamori... wonder if she would believe hearing the MC doesn't need to be saved.
OFC WHY WOULDNT SHE WANT TO WORK THE PEOPLE WHO WERE WILLING TO KILL HER TO HET TO HIM!? Who do she think she is
She really think she about to storm the enemy base and save the "princess" and live happily ever after
huh? did they brainwash her or something? she went from being carelessly held as hostage and bait, to working for them? she thinks the exorcists are good now? and that monoma was kidnapped by monsters? wtf