You haven't chosen a very easy passage.
"I have sought it, finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined."
The subject is "I" and what "I have seen" is the prefiguring vision of heaven as imagined by saints in poets. Further, he saw it "in a mystic miniature" and it was seen in the union of love. Does that help you figure out the complete predicate?
"And I have tried to apprehend the Pythagorean power by which number holds sway above the flux."-- what's the meaning of "number holds sway above the flux" - With Russell, it's anyone's guess. Well, no, I'm sure scholars aren't guessing, but I find his writing almost incomprehensible.
"But always pity brought me back to earth."
Is "But pity always brought me back to earth" also grammatically correct?
It's poetic. Usually you'd find the "always" before the verb, not the subject, and starting with a "but" is not "standard" but literary in this sense.
"helpless old people a hated burden to their sons"-- Do/does helpless old people depict many old people or just one person? if many, why put "a hated burden" instead of "hated burdens"?
He refers to the general concept of "old people" but each set of parents is only one burden to any one son.
"the whole world of loneliness, poverty, and pain make a mockery of what human life should be" --should "make" be "makes" since it's referring to "the whole world"?
I believe you're right!