If we can trust Google hits then it's George Bernard Shaw. Skimming some sites that pop up when searching for Oscar Wilde and Winston Churchill I recognized that all those pages do have one in common: They either conclude "No, they didn't" or "Whoever it said".
To pick some examples where George Bernard Shaw is named as origin:
The first source discussing differences between British and American English and how the division evolved states George Bernard Shaw as origin.
The Irish writer George Bernard Shaw once said: 'England and America are two countries divided by a common language'
And here again George Bernard Shaw is stated as origin but the other names are also mentioned.
Well, it likely is Shaw, actually, who said “England and America are two countries separated by the same language.” And you can quote him on that, because he also has been credited with saying, “I often quote myself. It adds spice to my conversation.”
Well, about the second part of your question. I don't think so. I live in Germany and with Austria and Switzerland there are two countries which do speak the same (or just a similar) language. But I've never heard that sentence in relation to these countries.
Besides the mentioned example I can't, off the top of my head, think of any other countries where it could be likely to be used as well, thus I conclude:
Yes, it's the only usage in the context of Britain and America.
The late Joel Buchsbaum, who was the media's first NFL draft expert, and possibly still its best ever, has been credited with originating this phrase. He also used another one I like, "all-pro from the neck down".
Best Answer
The noun, 'come-hither', derives from the verbal phrase, 'come hither'. The first attestation as a noun shown in OED Online is from 1900:
["come-hither, n.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/36850?rskey=ziZqlA&result=2&isAdvanced=false (accessed September 14, 2016).]
Much earlier attestation is readily found with contemporary popular news archive searches, wherein the noun is often used with 'put':
(The Moreton Bay Courier, Brisbane, Qld., Wed 3 Aug 1859.)
In these uses the derivation from the verbal phrase is quite evident.
The noun form cross-referenced in OED Online, 'comether', represents a dialectal pronunciation of 'come-hither':
["comether, n.". OED Online. September 2016. Oxford University Press. http://www.oed.com/view/Entry/36878 (accessed September 14, 2016).]
An earlier attestation for 'comether' than that given by OED Online is also available through the aforementioned news archive searches:
(The Sydney Gazette and New South Wales Advertiser, Tue 29 Dec 1835.)
Further investigation with specialized dialect resources may reveal regional sources (from the evidence shown, Ireland) as well as earlier attestations.