Pew Research Center: 2. Behaviors people find acceptable and unacceptable in men
When it comes to how Americans view certain behaviors in men, most say they personally think it’s not too or not at all acceptable for men to: Four-in-ten also think it’s unacceptable for men to play ...
'Acceptable to' is not really used in this situation. 'Approved by' and 'accepted by' are both perfectly fine, although I think 'approved' is a more typical usage. As a side note, program and report are not proper nouns, so they should not be written with a capital letter.
According to the Wikipedia article entitled "Manual of Style (abbreviations)", N/A is the only one that is proper; however, according to the Wikipedia article entitled "n/a" ("Not applicable" redirects to "n/a"), all of the other forms are also acceptable.
I also add that in AmE it is acceptable to use friendly both as an adverb and as a noun. There may an example in which 'friendly' is an adverb, but ordinarily it is not an adverb. It is an adjective. In general the rule about the number of syllables predicts what English speakers say, but not always.
Yes you can, depending on the type of document. I wouldn't suggest you use abbreviations in formal writings, but in tables, graphs, etc., abbreviations are acceptable.
Do you mean the young woman over there?), young woman is more acceptable than young lady. But in that Obama quote, where he’s picking out a member of the audience (in what’s obviously meant as a polite way), I expect however he referred to her it would upset somebody!