Learn English – Origin of square and cube as verbs

In the meanings you cite, jimmy is from 1848, jack is American English from 1904, peter out is miners' slang from 1846, and the two johns are from 1932 and 1911, respectively.

The only connection I was able to find between any two of them is this:

john "toilet," 1932, probably from jack, jakes, used for "toilet" since 16c. (see jack).

As to the aside, yes, it does happen in other languages, too. As the most obvious example off the top of my head, the Russian derogative term for a German is фриц (Fritz), and the German derogative term for a Russian is Iwan (Ivan).

Edit: seanyboy's answer made me revisit peter out, and it is indeed not clear whether it is connected to the name Peter at all. Etymonline says:

peter (v.) "cease, stop," 1812, of uncertain origin. To peter out "become exhausted," is 1846 as miners' slang.

Wiktionary adds:

Various speculative etymologies have been suggested. One suggestion is that it comes from peter being an abbreviation of saltpeter, the key ingredient in gunpowder – when a mine was exhausted, it was “petered”. Other derivations are from St. Peter (from sense of “rock”), or French péter (“to fart”).

A. 3-meter-square area & B. 3-square-meter area is what you are after; the hyphens bind together all the elements they connect into a single adjectival unit of meaning.

Area of 3 meters squared would not take the hyphens, because that expression is constructed in such a manner that its elements are not bound together in the same way.