This version of the R was only used in ligatures, but in modern times they were looking for a fast cursive and re-introduced this letterform and gave it a completely unhistorical upstroke, so that they could use it in their writings. So this "r" is in reality a "R" from the end of a word and it's missing its vertical stem.
Palaeographically speaking this "r" (your number 2) is utter nonsense, but it's serving a purpose nonetheless.
The "2" version of the r was originally written only after curved letters so that the curve of the previous letter could serve as the stem of the r, but somewhere around the middle of the Gothic hands, scribes started writing it after any old letter. (Cue elderly monks grumbling about the decline of standards among kids these days.) It stuck around through the formal Gothic hands, through the Gothic Cursive hands, and into Ronde and its Continental descendants. I don't know when the 2 developed an upstroke and became the cursive r we know today, but the late 18th-century <i>The Encyclopedia of Diderot & d'Alembert</i> shows the full modern form: http://artflx.uchica...te_19_21_9.jpeg
Meanwhile, the U.K. decided Ronde-style hands were too elegant and legible, and veered off into Secretary Hand. They developed a double-stemmed r that was unlike anything on earth, and difficult to boot. After struggling with that for a few centuries, they gave in and took up Italic, but initially seem to have preferred the "classic" lowercase r--don't quote me on that, but I do recall Dr. John Dee himself as having a most refined Italic hand, with only the classic r. The U.K. probably reimported the cursive r from France shortly after that, and thus do we arrive at our current state of confusion and bewilderment.
Personally, I can't see the outlines of the classic r in either of the cursive r's. That doesn't stop me from using the cursive r, but until I took up paleography, it didn't occur to me that the cursive letter had anything to do with the "real" letter. It was just one of those weird things they made you do in school, like calisthenics.