What would the opposite of "帰属意識" be? I simply don't know enough about the Japanese language to figure it out myself. Basically, what I'm looking for is 'a sense of not belonging.'
As for your second request..
That also is correct [i think]
I believe you could also say
生き甲斐が未知です
that would be like saying:
[the, my] purpose in life is not yet known
whereas
未知の生き甲斐
would be more like a whole noun meaning：
[the] unknown purpose in life.
I hope that makes sense.
I am also not sure if any of this is accurate or common Japanese because I am still learning Japanese myself, so I'd recommend waiting for someone more knowledgeable than I to post and make sure that's right
未知 literally means not yet known but can also be "infinite" in the positive sense.
So, 未知の生き甲斐 can be what you suggest or "infinite" purpose in life, depending on context.
Typical example is 未知の可能性 (infinite possibilities).
Yes, that's about right.
Not exactly antonym, but there is 疎外感 (sogai-kan, sense of alienation)
未知 literally means not yet known but can also be "infinite" in the positive sense.
So, 未知の生き甲斐 can be what you suggest or "infinite" purpose in life, depending on context.
Typical example is 未知の可能性 (infinite possibilities).
HTH!