1)
~ものも~ない is an idiom, meaning the situation that should normally happen / occur changes to the opposite one.
e.g.
嫌いな人と食べると、おいしいものもおいしくない。
捕まえられるはずだったのにもう捕まえられなくなった makes sense, maybe?
2) a)
even
b)
I think it's more likely contrastive. It's not "easily", but not "impossible" either.
3)
Hmm, there might be some difference in the usage, but it would be hard to answer it without reading the book. Generally, 一角獣 would sound more literary or archaic than ユニコーン, jimo.