There's 1 more chapter and IF which, from what I heard, is an alternate ending. I meant wrap up as in how they'll end the story, how this whole time leaping stuff works, and if Umeko really just a future time leaping Sakura, etc.
Trinitia scans, the previous (current?) group, has scans up to chapter 47 on their site. Not sure why they haven't uploaded it here, though. Pretty annoying having to juggle through a bunch of group sites just to remember what stuff is being updated.
In the context of things, Akira is just marking Kotaro as hers but our dense MC is focusing on the literal words (spit). https://jisho.org/search/%E5%94%BE%E3%82%92%E4%BB%98%E3%81%91%E3%82%8B and https://kano.ac/posts/2017-11-23_10-56.html for some information on its usage. I'm only a Genki Lvl...
Considering she mentions "dolls," I'll assume that her skill is more so controlling puppets/marionettes (or maybe even necromancy) and thus the whole "Life Bestowal" (生命付与) meaning. This is purely off the context clues. Maybe a raw reader can clear this up.