The word “reasons” doesn’t need an article/determiner because it’s followed by a reduced restrictive subordinate clause (still obscure). It could be rephrased as follows: “… for reasons that are still obscure, other people do not notice the smell.”

Yes, it does. No determiner is ever required with indefinite plural nouns.

yes, 'for reasons' means the same as 'for some reasons'. However, since English speakers usually try to say everything as quickly as possible and since in this situation, 'some', isn't a word that adds more meaning as far as most people are concerned, it is okay to omit 'some'. Also, 'reasons' is plural, so it already informs you that there may be more than one reason.

Yes, it means for more than one reason

Based on some causes or facts