Where does she go to tap the guy and how does she get there?

There is a carriage which will ostensibly be taking them to visit a florist who lives a block away.

...if that's necessary, okay.

"Unfortunately, yes - even going without an escort following us into the florist's shop is a privilege I am lucky to have." She doesn't seem especially enthused about this.

"An escort? Who would be escorting you if you were less privileged in this way?"

"A married woman or male relative."

"Sounds inconvenient to need to source one every time you want to go on an errand."

"Noble ladies don't normally need to go on errands."

"Isn't it tedious to have to describe in advance exactly what - if you were going to the florist - flowers you want, and what to get if they don't have those, to someone who goes in your place? You don't get to browse, that way. I, uh, will probably never really appreciate a flower again, and was not actually much of a flower-buyer before either, but I think a lot of the appeal would be in the browsing."

"Yes, most unmarried noble women would need an escort if they wished to browse - it's not a tradition I find myself fond of."

"Well. Fortunately we are - privileged."

"Fortunately."

The surgery is apparently set to take place in someone's living room - the surgeons still unpacking once they get there, next to his terrified patient with a swollen arm. 

"Hello," Annie says to the man with the fucked up arm. "How much has been explained to you already?"

"You have some nonsense abilities which might help me not die, and might permanently fuck me up in some different way."

"I am hoping I can avoid anything I do to you being permanent. What I can do is I can give you a good thing and a bad thing, together. I think I can also take them back but I haven't tried it before. They're all things I have, so none of them will kill you. I don't know which ones go with which other ones, though. So I'm going to try giving you some of the bad things, and you can try to tell us what went with them; that way I can avoid the ones that would be permanent. If none of those are the healing one, I'll try giving you the healing, but it could send you to another universe, or it could make you fall in love with someone, and in the first case I won't be able to undo it because we'll be in separate universes, and in the second case I'm not sure if it will be possible for me to take it back. Does that make sense?"

"Enough sense - anything to get a better shot at this."

"Okay. Do you want to start with being blind and deaf or with being too hot?"

"Too hot."

Poke: too hot.

The swelling on the man's arm goes down a small amount immediately.

"...huh, I think that might have helped your arm? Does it feel like it helped? My healing was faster than that but we can leave this for a bit and see if it makes more progress."

"It feels less tight and itchy? Could be less warm too but that might just be everything else being warmer."

"Let's wait a little and see if it'll heal your arm, then..."

It does actually improve a little more, but so slowly that Annie asks if he'd be willing to get a small nick on his skin somewhere to see if that heals too, to distinguish between "the healing power doesn't work very well on infections" and "this is not the healing power at all".

Sure - if it's not going to go down any more than this he'll have to get a much bigger nick.