My question is: why would the master cries before the immolation?
The "Winter" segment of the movie kind of gave the hint. Notice in this segment, after being paroled from prison for the crime of killing his wife, the now middle-age apprentice returns to the floating monastery and begins to take on the role of his previous master. And as with the movie's title's central theme, which reflects the cyclical nature of Samsara, the same exact history repeats itself with the scene of a woman abandoning her baby son, then the baby becomes the boy apprentice who is shown tormenting a turtle in the Spring-Again segment,... etc. Putting together all the pieces of the puzzle, it points to the original old master's own dark past with its own dark kamma before he renounced it to become a good monk. So although after years of training and gaining certain level of attainment, he's still not free of his kammic debt. And so he cries not only out of sadness for his student but also for himself, that his self immolation doesn't mean total and final complete liberation, there's still "more work to be done" and life will go on and on until all kammic debts' been completedly exhausted, hence the image of the water snake swimming away after the self immolation.