I’m not sure what the raws say since I haven’t seen them, but considering “oba-san” can mean either “aunt” (blood related) or a respectful way to refer to an older woman
Aunt can be written as 叔母さん or 伯母さん, and older woman as 小母さん, if the author wants to be 100% clear. Here it's spelled with kana (おばさん), which can refer to all three, so technically it's ambiguous. However, the obvious reading is still aunt. E.g. here ("That's what my aunt told me"), she uses just oba-san without any explanation. If she meant "old lady", the conversation wouldn't make sense.
I’m pretty sure Indou was just a stray puppy picked up by Kagami’s mother.
Shinobu's and Kagami's mothers were both army officers. The simplest explanation is they knew each other, and that's how Shinobu and "Auntie" know each other too.
Now, "Auntie" was the one who recommended the Academy. Why didn't she just take Shinobu in? I don't think it would be controversial to adopt the daughter of a well-known officer, and it's not like they have money issues... Find out in the next chapter, I guess.