Anyway... this is just about where my knowledge drops off, I think, here. It's clear to me that Tsukasa is a normal girl that drank the immortality elixir from the end of the folklore tale about Kaguya-hime. A normal human like her, especially one that goes through a traumatic event like I heavily suspect she has to receive that elixir, would wish for her suffering to end, but because of the elixir, she can't end it. She will just virtually instantly heal any attempts to harm herself.
The pain and suffering she must have gone through over the ages since that time... I can only imagine, immortality is, in many ways, a curse. It has frequently been depicted as such in fiction, and it is no surprise why for many people with good hearts: you will have to watch everyone and everything that you ever cared about perish and fade away, while you persist.
A life lived like that would harden even the softest of hearts, so it's no surprise she's as eccentric as she is. As reluctant to get close as she is. But she presses forward because she has actually fallen for Nasa.
All this to say... Tsukasa isn't all that 'strange' when you think about the kind of life she must have lived as a normal human given immortality suddenly. She still has her human compassion and emotions, but they are hidden beneath layers of emotional defenses to protect her tender maiden heart.
Immortality also easily explains why she's so adept at so many things: when you have all the time in the world, you can spend it perfecting as many crafts as you so desire.
Edit: Whoops... looks like the next chapter was something I remembered about, as well... heheh... Ah, that finally rears its head, now, as well.
