I was looking at example sentences for 「気づく」 to determine which particle it uses and I found that it takes 「に」. For example: 「彼はそれに間もなく気づくだろう」. However, I also found these sentences: 「私は彼が有名人だと気づく」 and 「自分が一人であるのに気づく」.
Firstly, I'm struggling to analyse 「一人であるのに気づく」; 一人 (noun) + であるの (nominaliser) + に気づく is this correct? I thought that you only used である with こと (e.g. 先生であること), but you use な with の (e.g. 先生なの).
Secondly, I have no clue what 「だと」 means in the other example. Again, it looks like a nominalised sentence to me, but I'm not sure how 「だと」 is used. Even if it was nominalised, why is と used and not に?