Yes, a good cry is somewhat idiomatic. The phrase has been around for quite some time, too. An 1869 magazine article read:
Completely overcome by chagrin and disappointment, I had a good cry over it.
and in an 1887 issue of Harper's:
How often in her own room, distracted between those conflicting fears and hopes, she sat down with her face between her hands and had a good cry over it!
More recently, in a 2004 novel by Steve Tesich:
He had a good cry over it and it made him feel better. Made him feel good again. Good and heartbroken. Good and scared. But basically good. He was feeling good about something again.
So, what is a good cry? The website AgingCare.com offers a hint:
Researchers have proven what many caregivers have already figured out on their own: sometimes there's nothing like a good cry to make you feel better. Crying is cathartic.
We can cry about a lot of things, but a "good cry" will make us feel somewhat rejuvenated and emotionally cleansed. When comparing the improved moods of criers as compared to their more "stoic" peers, one researcher said:
This pattern is often found in retrospective studies where people are asked to rate their mood levels after having experienced a good cry.
Going back to your original sentence, it's hard to say for sure why the person cried – not without knowing what was in the letter. Whatever emotion triggered the tears, though, we know it was a good cry, meaning that the cry was deep, and that some emotions were released to the point where the person felt "cleansed" afterward.
As we can see from its -ly ending, fastly is an adverb (if it weren't a proper name). Error is a noun. Adverbs do not modify nouns, and so "fastly error" would be ungrammatical.
The namers of the company may have thought themselves clever, but their error message makes no sense to anyone who is not familiar with the company. The error itself seems an error.
Best Answer
The construction you should be looking at is not "as having" but "quoted as V-ing". Remember: "as" and "like" mean "similar to".
It might be easier to explain to put it in a complete sentence:
Celebrities who have been quoted as having used Widgets now regret endorsing the products.
"Who have been quoted as having used Widgets" means the celebrities have said something similar to "I have used a Widget" (proper, correct English) but maybe not those exact words. Perhaps they said: "Widgets? Yeah, I used one" or "I love my Widget!" or "Widgets are wonderful!" or "I have a Widget in every room in my house."
In WS2's examples, Mary may have said, "Of course ghosts are real!" But when we state it as an indirect quote, we might say 'Mary is reported as believing in ghosts'--similar words with the same meaning.