She will have no trouble affording her hotel room!

...she might have some trouble keeping a low profile, if that is a goal of hers.

Not necessarily.

She does listen for and ask questions during any conversations in which the Emperor is mentioned.

Inconveniently, people within human hearing range of her singing mostly don't talk. But when she listens farther away than that, or spends time not singing, she can overhear Emperor-related gossip such as:

• remember that time he threw somebody off the palace roof a few years ago? Working at the palace must be terrifying!
  
• they finally tore down my old neighbourhood and the Emperor came in and built new houses overnight and they're all gorgeous
  
• my friend's cousin's husband sold one of his maids last year and the Emperor bought her, poor girl
  
• it's been a while since the Emperor added new land to the island, I wonder where he'll put it on next?
  
• I was at a party last month, more upscale than I usually go to, and the Emperor showed up, but people mostly weren't frightened - maybe you get used to it, if you run in the sort of social circle where the Emperor shows up to parties - anyway I left early and I'm not accepting any more invitations from that household, maybe some people can get used to socializing with the Emperor but I'm not cut out for it
  
• my uncle's girlfriend's sister is a palace secretary and she says it's just like any other job really, but she doesn't dare go near the Emperor's personal wing because she took a shortcut right past it once and she could hear the girls screaming, which doesn't sound much like any other job to me
  
• my ex-landlord's family fell on hard times and had to sell his niece, and he ran into her in the market and she said it was so awful she'd rather belong to the Emperor, I'm sure she didn't mean it but can you imagine—!

Hm.

She goes for a meandering walk that takes her past the palace twice. She listens.

Assorted governmental sounds from the more public sections. From the Emperor's quarters - it doesn't sound like he's home right now, but there are a handful of women in his section of the palace, and two of them are crying while the third quietly eats lunch.

Hmm.

She busks on a daily basis but at different times, and takes walks past the palace every day, at different times.

The Emperor is, variously: out, napping, napping, torturing someone, out, out, descending from the sky on huge grey owl's wings and landing on a balcony as she watches (and then taking a nap), torturing someone again, and in the public section of the palace having a conversation with some sort of bureaucrat.

"I don't see why you want me involved."

  "I thought you might like a chance to comment, all things considered."

"He annoys me. I don't have people executed for annoying me."

  "...well..."

"'Well' what? That incorrigible pest from a few years ago? I threw him off a roof; the law of the empire did not at any point get involved."

  "...fair enough."

"I have no idea whether Lord Estulas defrauded all those merchants and no particular urge to find out. Leave me out of it."

  "Very well. And I assume you're equally uninterested in looking over the proposed changes to tax law—"

"Tax law does much better without my input. I'm going to go redesign my bedroom or something. Send for me if you think of anything that could actually benefit from my attention."

And then he does in fact go back to his wing of the palace and reshape a sizeable chunk of it into a new but equally beautiful form.

She sings, and reads books about everything especially magic, and walks past the palace.

And, having seen him land on his balcony that one time, she'll probably recognize him despite the lack of wings when he comes by to listen to her sing.

Nobody else seems to catch on; he doesn't attract any more attention than any other listener approximately that well-dressed. After a few songs, he comes up and drops some very high-denomination coins in her basket.

"Thank you."

"Welcome. Where'd you get a voice like that?"

"It's nothing special where I'm from."

"Oh? And where's that?"

"It's called Valinor. I can't get home; I arrived here by accident."

"Sorry to hear it. You must really be fed up with our idea of music by now."

"It's stylistically novel and some of your people are skilled."

He giggles. "Is that like telling your neighbour that the lime-green curtains have character, or do you actually see some merit in it?"

"It's more like telling a child they have promise. It can be sincere without measuring absolutely."

"Fair enough. I'd better quit taking up your time, people are starting to be annoyed with me."

He tosses another coin in her basket and walks away.

And she sings another song, and walks by the palace.

Torturing somebody again.

Mm-hm.

She waits to see if he comes back the next day.

No, but he's back the day after that. With money again, even.

"Hello again."

"Was I that memorable?"