When deciding to test one's faith, sometimes the age old question of, "Do I really want to know?" is forgotten.
What does, "Do I really want to know?" have to do with the decision to test your faith.
Once you've decided to, haven't you already answered that question for yourself?
I don't understand what you mean there, so you could probably do a better job of explaining it, or make a new opening sentence.
Just on a side note, you use "sometimes" or a variant, 3 times in the first two lines.
"A man testing his faith cannot always see the impending danger in doing so."
Really, you can do a better job of explaining that. I think the man who is testing his faith has some idea of danger; maybe he just doesn't know how much the danger is, or he doesn't anticipate the nature of the danger and the deep effect it will have on him.
"After this life ... he knows to be good."
Are those people still good? That is what you imply. Maybe those are people he once thought were good?
"journey into
to the dark woods."
"He insists that... showing that ...too far."
Use better words to describe "showing that..." Maybe it hinted at his initial reluctance at going too far.
"Slowly but surely, the occurrences in the woods"
Replace occurrences to add clarity and diminish awkwardness.
"...curiosity. His faith..."
curiosity; his faith is waning, but not completely disintegrating.
"Slowly but surely, ... Goodman Brown's faith. The companion in the woods ... family line and village elders.
The problem here is that you don't do a good job of introducing the concept that his faith is being stripped away. See, you want to mention the degeneration in his faith, which you do, but you also want to avoid redundancy, and the delivery here counts towards how well your writing is received by the reader. The first sentence doesn't do an adequate job; it doesn't use good enough words, and it is clipped. These two sentences are noticeably backwards, and they will hurt you. It's not good regardless of the circumstances, but more so when you are telling us an important detail. You need to vary these two sentences so they are worth in their own respect, and also make sure to coalesce them into each other.
Here's how I might revise it.
Slowly but surely, the occurrences in the woods start to whittle away at the base of Goodman Brown's faith. The companion in the woods takes it upon himself to chip away at one important piece of security in Goodman Brown's faith: the righteousness of his family line and village elders.
Remember to keep in mind that you said his faith was "waning, but not disintegrating."
So now you want to add the element that some factors are contributing to the increase in the rate at which his faith is becoming unravled.
As Goodman Brown ventures deeper into the woods, due to a series of events, we get a sense that his faith is now capitulating in earnest. Those events as we come to know, are caused by his companion; they rip into a central component of Goodman Brown's faith: the righteousness of his family line and village elders.
I'm going to have to cut it short here.
Just fix the rest of your essay to the tune of these revisions and you should do fine.
Mustafa