Is it okay for Rangiku to...
1) Sense that your character has spiritual/soul related powers?
2) Be disturbingly insightful into whatever issues get naturally revealed about your character in conversation? Warning: This may result in hugging regardless of circumstances.
3) Troll the general hell out of them?
Is it okay to...
Threadhop?: Some good sense here - if it is SRS BZNESS, please PM first. If not, go for it!
Backtag?: Please!
Hug/Kiss/Glomp?: ...despite being as she is, Rangiku is actually very protective about her personal space with people she doesn't know, if she's not in control. And sometimes even when she's friends with you, if you're male and hanging onto her she'll get abruptly tired of it and shove you off. She's nicer to girls. But she comes from a very formal society... and so, yes, go for it by all means - just be prepared for awkward.
...something more?: If you go for the grope, be prepared to deal the consequences - pissed superhuman strength.
Romantic Relationship?: ...yeah, doubtful. Open to possibilities, though.
Maim/Wound/Scar?: She canonically gets hurt all the time when she goes up against people who are stronger than her... which she does on a fairly regular basis. So if your character can tear out her ribs seriously wound her? Go for it. I'd just rather not have anything lethal dished out without plot.
Kill?: No; unless it's something we've worked out prior (i.e. for a drop/plot).