Different versions of lowercase R

Is this something unacceptable in cases like exams or assignment submissions?

No, it is of course acceptable, as long as your handwriting is legible and understandable. In English, there are two different ways to hand-write a lowercase "r": the cursive way and the non-cursive way. Both are fine as long as you write them clearly, and both are interchangeable as well.

do others also exhibit such behaviour in English handwriting?

Yes. As others have mentioned, handwriting is up to the individual who is writing. It can change at any moment's notice and you can do whatever you want with it. As long as it's legible, it's fine.