Those expressions mean respectively to pass and to fail an exam. I have the feeling that those expressions convey something that is not in the neutral verbs to pass and to fail. That is to say that 桜{さくら}咲{さ}く seems to mean "to pass with flying colors" and 桜{さくら}散{ち}る to fail but the person who fail is a bit disillusioned because of his/her failure.
Are those guesses right ? And could they be used in a general sense of "to success / to do well" and "to fail" at a task or are they reserved for exams.
I did some research and it seems to be that those expressions are used exclusively about exams (and especially university entrance exams) and nothing else. According to my research, the expression was coined by the Waseda university in 昭和31年(1956), if you passed their exams your telegram reads サクラサク and if you failed it reads サクラチル.
Some other universities borrowed a leaf out of Waseda's book and it seems that each university has its representative way to express "to pass" and "to fail" at their entrance exams (cf. this link)