Nagato speaks in older casual style, which gives her a bit of a formal air; I tried to replicate that in the second text block by puffing 'give' to something more reverent. 'Hajimete mo . . . sasageru" I figured was reasonable, given the tears and context, to be her first time, sexually, but I suppose it could have also been "from the start, my intention was to give [something] to you" instead. Usually, that's "hajimete kara" but again, Nagato's speech is a bit direct. Still, I suspect this is probably the intended meaning?
Which, really, kind of suggests even she isn't fully aware of what's happened. Her eyes also don't look A-OK here... Do date rape drugs work on shipgirls? Seems like that kind of situation.
Updated
You want to see my panties? Since it's a request by my beloved, I can't refuse. There, is this okay?I am, of course, your possession; as such, my intention is to dedicate to you my first.
Hm? What could be the matter?