Useful for "eye-balling" the status of a process or whatever. But: No way to trigger a command (automatically) upon a condition, and Do you really want to sit there and watch for files to come in? If you do, then :

Code:

watch ls -l $MAILBOX

is fine.

Never. You'd have to kill the process. It's equivalent to removing the while loop and putting the script as a cron job that runs ever 5 minutes.

It's running the pipeline of ls and grep. The grep is looking for any line. If ls finds no files, it outputs no line, and the grep search fails. If the grep search fails, it exits with 1 which (in BASH logic) means false, and so the if condition fails. If the grep finds at least one line, this means there are files and so the if condition succeeds and the THEN portion is executed.

Are there other files in the directory besides these?

There are at least four solutions to this. In the worst case, you can use what is suggested by ddreggors. Here are solutions to try:
ddreggors solution is a bit resource-intensive, and VERY linux-specific, but it will work if the uploading process does not close/reopen the file in between writes AND if it removes the file after failure (if the upload process is interrupted and the file is not completely transferred). It will fail if there are any other benign processes reading the incoming files. Here is a re-write of that solution which is more efficient (ie, doesn't use additional forks):

Code:

cd $MAILBOX
LSOF=/usr/sbin/lsof
for f in *.dat; do
  if  $LSOF $MAILBOX/$f ; then
     # trigger action goes here.
     sftp $MAILBOX/$f someone@somewhere:destination/$f
  fi
done