Main sentence:"I'm afraid of telling him out of fear of rejection"
Question about above sentence on Past tense:
"Was She afraid he would say no?"
That's right, yes. She was afraid of rejection.
In the mentioned sentence 'He would say' mean:
1-Would imagine, say, think, etc. (that)… used to give opinions that you are not certain about?
2-Would is past of 'will'?
Sshe afraid he would say no [if she asked him]?(And, as 5jj said, in that context "will"'s back-shifted)
'She' is a character in King Solomon's Mines.