She makes an illusion of one of the throwing stars she has, then dissipates it. "Also how I'm speaking your language." (Not generally an effective use of her time, this, but it is useful to have more of an idea of various people here, and possibly of how information spreads.) 

"Huh. Chakra doesn't do language, though the Yamanaka might be able to skip that," Tobirama says.

Madara's eyes went red at her illusion. "...I couldn't see through that," he says uneasily.

"It makes sense that magic illusions would work differently than our illusion techniques. Guess your eyes aren't everything, Uchiha," Tobirama says somewhat frostily.

"Can you generally see through illusions?" (If she extends senses, can she detect anything about his eyes?)

Slow nod. (His eyes have a significant concentration of chakra in them.)

"Ah. How so? And I have been earlier informed that the illusions in this world work differently." (Anything more detailed?)

Hard to say. The flow's definitely active, and subsides once his eyes go back to their normal color, but doesn't cut out entirely.

"You're not an Uchiha. I'm not telling you that," Madara says.

She notes this to inquire about later. Notes the apparently sociological feature.

Are they continuing to talk to her after that?

They seem to be getting bored with the conversation, though Tobirama's less bored and more frustrated.

Then she will go back to the book room(s).

The boys lapse into arguing, then go back to exercising.

The book rooms are still there, in all their barely organized glory.

She notes subjects and the like. 

Physical fighting reading she has some interest in, and she should take a look at for what-she-might expect purposes, but is not particularly urgent - if she gets into a physical fight with someone at the moment for some reason, her primary advantage will not be physical fighting related. 

Magic she continues to have great interest in but is for study rather than immediate urgency.

Anatomy, some of botany and sociology and zoology a primary question is to what extent it is the same, and where it is then where their knowledge of it is. (It's not impossible that they have knowledge her world does not, but from various indications of technology level and such she is generally expecting mostly the other direction). (And, is there mathematics? Physics? Chemistry? Biology?)

History, geography, the other parts of botany and zoology and sociology she does not expect to know at all, and that is a priority. History, geography, sociology particularly so. (She takes the catalog of clans).

She will look for general and overview books, and start skimming for the anatomy etc questions.

Chemistry still seems to be fairly theoretic, and early, though probably closer to correct that what her world produced in its early days. More incomplete than wrong. There's mathematics, which checks out, and which is more advanced than world technology levels would suggest, but not as advanced as her world's. Physics, yes, though it looks like someone pasted very early physics textbooks together with textbooks on advanced studies on n-dimensional space. Biology is advanced, not equal with her world but close, and it looks like their anatomy might be slightly different - they have 'chakra pathways' and 'chakra points'. The more advanced books are a mixture of fifty different handwritings, with scribbling in the margins, and new-looking all in the same handwriting (these seem to be compilations of information from the less organized books, stripping out the contradictory and proven wrong). Several of the older books disagree with each other, and contain shaky or dubious if not outright inaccurate information.

The general and overview books are either meant for children, or in the same handwriting as the properly organized advanced books - as if they've only recently started compiling their information. 

N-dimensional space and chakra anatomy are interesting. Metadata is - probably sociologically informative. She notes their mathematical notations. She notes the handwriting, in case she encounters it before she encounters a chance to ask about the writer.

She has not previously found herself in handwritten libraries of other worlds, but research skills and experience are generally applicable. She makes organizational schemas, and organizes overview and reading plans, and reads.

There is a lot of information crammed into the books. Much of it contradicted by notes in the margins, or other books. 

Overall, though, they seem to have fairly similar biologies, and some similar animals and plants, some different.

She notes information. She notes contradictory information and considers what if any inquiry, experimental or otherwise, might yield the accurate answer. She reads.

History is pretty much in three categories: distant myth, dynastic history (a lot of this is a record of who killed whom), and what's likely an attempt at recording more recent oral history plus teasing out events from scarce records. It mostly paints a picture of a fairly unstable society dominated by warring nobles and mercenary clans, although going back about a century it looks like the area used to be more-or-less unified under an emperor, the last of whom was assassinated along with his heirs by one of his retainers. Who was in turn assassinated by another noble, who seized the throne then fell in battle four years later, spelling the end of the empire.

She sees.

How far back does their history go? What extent of the world does it cover?

Dynastic and imperial history only stretches back a few centuries, becoming more and more thin as time progresses. The most recent time mentioned as mythical is a mere thousand years before, when the main polities were the Land of This, the Land of That, and the Land of Ancestors. There's a discussion of the mythological Princess Kaguya, who supposedly united the world under her banner, only to fall to the Ten Tails along with her empire.

History mostly covers the eastern half of the continent; everywhere to the west of the great desert or across the seas is as shrouded in myth as the distant past, though there's indications that the recent empire had sea trade with other countries.

The Ten Tails?

Anything interesting out of the trade, or suggestive out of the myth?

Apparently an enormous monster that appeared and rearranged the continent, only to be defeated by the Sage of Six Paths. The myth links the monster's appearance to Kaguya's violation of the taboo around the God Tree.

Nothing super interesting in the trade itself; spices and gold and salt came from various directions, wood and silk and cotton went out. Apparently a number of industries and cities collapsed with the loss of trade, but that was a while ago.

Any details on the defeating?

What taboo and violation would this be?

Any indications of the culture and so on of the traded-with places?

It was a great battle that raged across continents for three days without end, until at the dawn of the fourth day the Sage struck down the beast. Unable to kill it, he sealed away its soul, and threw its body into the sky, creating the moon.

The taboo, after some digging and inference, probably refers to eating the Tree's fruit.

Traded with places are strange and exotic! They don't wear enough clothes, or all wear voluminous silks, their women are all kunoichi who will seduce then either steal from or murder you (it's hard to tell, but this seems to be a compliment, rather than fear-mongering about Those People, since it's followed by claiming that the women of the writer's people have grown soft), they're thieves, they're more honorable than samurai, they have fantastical abilities focused around amulets, they only use seals for their techniques, they call upon strange deities and don't properly acknowledge the spirits, their leader is a cannibal, their leader lets his council make all his decisions, their warriors are mighty and properly trained since childhood, they're fools who don't let their women fight in direct combat...

Was there something in particular that allowed the final striking down? (Also, 'rearranged the content'?) What did the Sage do subsequently?

Is there more information on 'souls'? 

(Given her context, 'its body created the moon' to her is plausible as both myth and as accurate reporting. Is there further information about the moon?)

...the 'eating Tree's fruit' sounds rather similar to the story Rian mentioned about the Kaguya currently at large. Any further indication of overlap? What happened to this historical/mythical Kaguya?

Sounds about what one might expect from trade but poor contact. Has there been more recent contact? Any details on the amulets, or on the seals? What's this about deities and spirits?

There's a mention that the Ten Tails could turn mountains into valleys with a swipe of one tail, and raise tsunamis with another. Apparently the coastline and topography changed rather dramatically. What the Sage did next is apparently had children who just about every ninja clan claims some kind of descent from. (No one has actual proof of this claim). He also traveled the world teaching everyone how to use chakra, and created a world of peace.

There is no further information about the moon, no.

Most accounts don't have any further information, no. One claims that she was found inside the stalk of a glowing bamboo plant by a bamboo-cutter and raised by him. She was of exceptional beauty and was courted by many princes. At the end of the story, she retires to the moon, leaving the earth mourning her departure. The story references an older tale that it assumes the reader has access to, claiming to be a historical analysis of a folk recounting; a copy of said tale isn't apparent in the library.

There's occasionally ships coming and going along the coast, but the fascination with the foreign seems to have faded since the fall of the empire, so nowhere available records anything about those ships.

Does 'teaching everyone to use chakra' reflect a lack of this knowledge previously? (Where did the Sage learn it?)

Their mourning was not affected by the Ten Tails incident? She retires to the moon which is a body, or is this a different moon? Is retiring to the moon a common story ending? Are there suggestions of what is imagined or considered to happen there? Are there other, especially non-story, records of people being born in plants and the like?

Any indication anywhere of how the other continents were or weren't affected by reported recent illusion-trapping events?