The superscript makes no difference at all. It depends on the 'house style' of the publishing house in question. Superscript used in this way strikes me as rather old-fashioned.

No. It really depends on your method of typing and whether you can make superscripts. In the US, we rarely use this form, using December 1, 2014 instead.

In the U.S. as Business English Ed says, we don't use ordinal numbers in dates. Style guides usually say to spell out "first" through "ninth." It doesn't matter if the endings are superscripted or not. The superscripted forms were once common in typeset text. With the arrival of typewriters, they became rare. With its default settings, Microsoft Word detects the endings and superscripts them, which is fine, but to my eye the superscripted forms look old-fashioned. In 2004, a clumsily forged document was quickly detected because it used a superscripted "-th," strongly suggesting that the document had been created with a modern word processor rather than a 1970s typewriter! See http://en.wikipedia.org/wiki/Killian_documents_controversy