TASK DEFINITION: Given the Question and Answer pair, detect whether the answer is acceptable or not. Denote acceptable answer as "yes", otherwise denote as "no". An acceptable answer is consistent with the context in question, detailed, long, and uses general knowledge of English. Answers that are not definite and suggest a variety of options are not acceptable answers.
PROBLEM: Question: It is common in American English to refer to a powerful person or organization as an 800 pound gorilla. The expression makes sense -- a gorilla of that size would certainly be intimidating -- but what's so special about the number 800? Searching "n lb gorilla" on Google for various values of n results in many more hits when n = 800 than when n is any other quantity. Also, the Google Ngram Viewer finds notable occurrences of the phrase "800 pound gorilla" in texts starting around the late 1970s; other sized gorillas don't seem to be mentioned at all. The Wikipedia entry for the idiom claims that the phrase is rooted in a riddle ("Where does an 800lb gorilla sleep?"), but that's just passing the buck. A 700lb or 900lb gorilla would be equally entitled to sleep wherever he wants to. Interestingly, the Wikipedia entry for gorilla states that the average male gorilla weighs about 400lb, occasionally reaching 500lb in the wild. Only obese gorillas in captivity have attained weights of 600lb. So the number doesn't even seem to be related to gorilla biology (except that it is safely larger than any known gorilla, save King Kong). Given that it's an arbitrary figure, is there any reason the number 800 would be more popular than any other? More generally, is there any relevant research into why some numbers would be more popular or pleasing than other in contexts like this? 
Answer: The answer to your question is No, there is no known reason for preferring 800 to any other number. I am not aware of any research into the question, but I haven't looked. Compare "The whole nine yards", "42", and "A Thousand Nights and a Night".

SOLUTION: no

PROBLEM: Question: When should whilst be used instead of while? For example, should I use the first or the second sentence? They don't do this whilst they do that. They don't do this while they do that. Which would be correct? 
Answer: I believe while and whilst are interchangeable, but whilst is more archaic and adds a nice flavoring to the sentence. That being said, "whilst" doesn't seem to come up so often in the middle of a sentence as you had it there, so I would use "while" in that case, even though both are grammatically correct. Whilst seems more apt to be put at the beginnings of sentences, e.g. Whilst going about my merry way I chanced upon a vagabond. Taking this serendipitous opportunity to satiate my bloodlust I decapitated him with a fork.

SOLUTION: yes

PROBLEM: Question: Should e.g. and i.e. have periods, e.g. "e.g.", or no periods, eg "eg"? Should they be italicized, e.g. "i.e." or not, eg "i.e"? 
Answer: In formal contexts, I would go with "e.g." and "i.e.", with two periods and without a whitespace. The spellings without periods are quite popular, but informal. For example, Merriam-Webster does not have an entry for either "eg" or "ie". Wiktionary marks "eg." and "eg" as informal, and offers the following usage notes: Opinion is mixed about whether this term should be italicized as although it is Latin, it has become part of standard English, and whether it should be written with a separating space "e. g." as it was originally two separate words. It also offers the following usage notes for "i.e.": Opinion is mixed about whether the abbreviation should be italicized, or whether there should be a separating non-breaking space as in i. e.. ie is often found in current usage, and is perhaps now considered acceptable. Personally, I would argue that there's no need whatsoever to italicize "e.g." or "i.e.". Both expressions are extremely common in English, and have been for a long time. They are full-fledged citizens of the English language, and as such, they do not have to be italicized as if they were foreign words.

SOLUTION:
yes