I don't have an opinion on tuition buyout yet - that depends on her opinion, the auction results, and future fief costs - and I think we're probably jumping the gun a little bit there. Let's walk through those steps first.
I will say, however, that I don't think we should view her as a sister at all. Even from an emotional point, Ling Qi is not ready to have a peer in a sibling role given the amount of trust and potential power over her that would entail. Maybe later (maybe), but there is a different between being in the same clan and being sisters. We're not adopting her into our family, especially since she's only bond 1 and is doing this as much out of self-interest as anything else. The closest analogue to how we should treat her is probably a combination of the Ma sisters and Li Suyin. She would technically be subordinate to us in this role, and we'd likely be responsible for some of her upkeep, but she'd also be doing her own thing within the confines of any strategic goal we'd give her.
I don't see this adoption as us becoming her guardian or anything of the sort, and we certainly don't have any obligation to buy her out. What I see this as is her essentially hitching her cart to our horse. While we should certainly take her opinions into account, she is ultimately responsible for her own decisions, and we shouldn't try anything like "making the decision for her because she doesn't know what's best for her" because she certainly does.
Being in a clan seems to mean support against external/large opponents such as other clans and resources, for the most part. I don't believe we're committing to anything more, nor do I believe we want to/should.
Essentially:
Hard disagree here. In order: the Sect isn't going to throw away greens (notice how they stopped before they were burnt out), you lose people in a war, it's condescending to assume responsibility for someone who currently is a peer, and we're making no such financial commitment to buying out her service - it's just an option.
I see where you're coming from here, but adoption into a clan is different that adoption by parents into a family, and Ling Qi would absolutely avoid the second one.