Are there any patterns whatsoever in what collections of lines correspond to what meanings, or is it entirely arbitrary?

There are some repeated components - the system did evolve over time, it wasn't designed whole cloth to be maximally confusing.

Then it has that advantage over memorizing the properties of three hundred kinds of tobacco ash. It's not as orderly as the Latin-derived names of every bone and muscle and nerve in the human body, and Watson will never complain about English orthography or Latin grammar again, but they both press on.

Miriqua is a very patient teacher.

They'll keep at this all day, minus the time it takes to get some lunch and bring it upstairs.

Lunch is served in the same way as breakfast; it's eggs and rolls.

They eat their eggs and rolls and go right back to studying.

Since the writing system is so difficult Miriqua focuses mostly on speaking, and occasionally writes notes for them in Latin characters.

They copy the notes into local characters for practice.

"- you need to be able to recognize thirty thousand characters to read a typical newspaper," she says.

"And probably even more to read a medical journal."

"Well, it would cover fewer topics, but you'd certainly need different characters for that," she says. "People created as children can learn it if they start then, but adult learners usually just get by with the spoken language."

"Are there enough of those that it's possible to be illiterate without being a burden on society? I do still hope to open a practice here."

"It's possible, yes."

"Then I think I'll get really good at the spoken language first," he says in the local language.

"Good. Once you know how to speak it you'll be able to ask almost anyone to read things for you, and until then I'm the only third party you can talk to," she says.

They keep up their lessons for the rest of the day, if Miriqua is willing. At some point they'll probably want to wander around outside getting used to voices and cadences other than hers, but it doesn't need to be this afternoon. 

Miriqua was literally made for this (among other things). She'll keep up with it to the extent of their stamina.

Outside people are bustling around distributing goods and services and social interactions to one another.

They can pick up on bits and pieces of conversations! Not as many as they could have in London, especially when the goods and services and social interactions are ones they don't have all the context for, but they're making progress. 

As one pays attention one becomes aware of a pretty bright line between proles and everyone else. There are more proles than there are everyone elses, but the latter are more attention-getting, have more and livelier conversations, once a pair are glimpsed to have a child with them, they have more complicated social relationships. The proles have work, they mostly talk about work, they mostly socialize with either people they know through work or the geographically nearest prole socialization locale. It's not that they're dim or lifeless. They are bright, lively people who, as it happens, really enjoy making shoes or sweeping streets or cooking meals or doing laundry for fourteen hours a day.

They both love their work, but only what feels like a reasonable human amount; the proles are a bit unsettling. How much time do the other type of people seem to spend working?

Varies widely. Non-prole work is less suspicious to be really fascinated by, anyway - research, the arts, governance and diplomacy. Some professions seem to have a mix of prole and non-prole practitioners, including medicine. It seems perfectly respectable for someone understood to be well-made but not aimed at anything that would (in a society with money) constitute gainful employment to bop around trying various hobbies and dabbling in things while living off the delightedly-provided prole labor.

Watson would be far to embarrassed to do that sort of thing himself if there's any way he can get gainful employment instead, but Holmes will appreciate being able to continue his Bohemian lifestyle of research and the violin. Or more likely some novel foreign instrument, since finding an actual violin here seems implausible.

There are novel foreign instruments to be had, though they seem to be mostly custom made rather than kept in stock; maybe he could get a violin if he described it well enough.

He can definitely describe a violin well enough, and will probably do that if it's that easy to get something custom. He will, however, resist the temptation until he has slightly more permanent lodging.