In the Book I, at what point in the allegory does it first become apparent that Pilgrim is a sinner under extreme conviction ?how do his relatives...

In my opinion, we find out that the Pilgrim is under extreme conviction about his sin in the very opening lines: "and as he read, he wept and trembled; and not being able longer to contain, he brake out with a lamentable cry, saying What shall I do?" And then later, after he goes home, he says it again, "What shall I do to be saved?" (read the text on the link below).

At first, his family is worried about him and hopes that he will feel better after he sleeps, but as he continues in his woe, they begin to get annoyed (hardened) with him.

The verses you refer to are all versions of the same Biblical promise - that in order to follow Christ, one must be willing to forsake everything, even one's family. These three verses (see the links below for Bible verses) all state that if a man follows God, even forsaking his family, he will be rewarded "a hundred times" and rewarded with eternal life.

A word of caution here, though. The Bible does not advocate forsaking one's family per se. This would be inconsistent with a myriad of other teachings in the Bible, i.e. "A man who provides not for his own is worse than an infidel" (1 Timothy 5:8). The idea in the Bible, as well as in Pilgrim's Progress, is that God must come first in our lives, even above our families. We can make idols out of good things, like our families, if we put them before God. If we do this, we might as well set up residence in the novel's Vanity Fair. The promise in those verses is eternal reward for following God, but following God does not mean forsaking our families, it just means that we need to put God first.