The word "convey" rhymes with "display" and can be associated with the idea of mystery in the sense of communicating or revealing hidden meanings or secrets. While it doesn't directly mean mystery, it can imply the act of sharing something enigmatic.
Yesterday is History, Tomorrow a Mystery, Today is
The word that means and rhymes with cloak is "joke."
The word "afraid" slant rhymes with the word "away" but means scared.
The word that means kneel and rhymes with melt is "knelt."
The word that rhymes with day and means sky is "gray."
The word that rhymes with angel and means free is "mangel."
The word that rhymes with "creed" and means the opposite of follow is "lead".
One word that rhymes with 'it' and means resist is 'pit'. In this instance the word 'pit' means to set in direct opposition.
The word "lean" fits your criteria as it means cool and rhymes with green.
The word that means a little wet and rhymes with "boist" is "moist."
The answer is weep. Weep rhymes with leap, and means to cry.