Regarding replacement batteries, you will find that OEM replacement-anythings are not produced or sold for any devices anymore, since the cost to employ repair technicians is now greater than the cost of producing a new device everywhere in the world. As a consequence, all replacement parts sold are stripped from existing devices. Because of this fact, the longer a device has been out of production, the less likely the possibility that you will find any wear and tear items in as-new condition. For screens, you will increasingly only find replacements that were polished to have scratches removed — along with the Gorilla coating (making them much more likely to collect grime and crack). For the Nexus 9, you will realistically not find a replacement battery with more, or even the same remaining capacity, vs the one you’re replacing. Again, keep in mind: we’re talking probabilities, not absolutes. Your friend may get a good part from a place one day and you won’t, the next day (or vice versa).

If you happen to own a Nexus 9 LTE model, I strongly suggest that you take a photo of the exposed back (i.e. with the rear cover removed) and all wires still in place. You will later find that the LTE model differs in terms of daughter boards used, apparent connection points, number of wires used, and most importantly the way the wires even connect various components. At that point, you will also find that guides that cover the WiFi-only model are useless, for said reasons. You will additionally find that the only guides that are commonly accessible cover only that model. Lastly, before you replace any of the boards, I also strongly encourage you to compare the photo you will have taken to any replacements, to ascertain that they are compatible (to get you started: you will note a connection point on the daughter board that houses the micro-USB connector present in the LTE edition and absent (although the board does contain the solder points forming a circle) in the WiFi edition).