Pausing & Aborting
Clicking the "Abort" button while sending is in progress will bring up a dialog asking if you really want to stop sending files.
While the abort dialog is displayed, the current file will continue to completion. No further transfers will begin until you answer the question.
If you confirm the abort, then the droplet will immediately stop any transfer in progress and send no further files. If you decline the abort, then transfers will continue.
Dragging the same folder onto a droplet again will resend all of the files in that folder, overwriting existing files with the same names. If, however, an individual file was interrupted part-way through its upload, then that upload may resume at the point of interruption.