Does a job scheduled in crontab run even when I log out

To debug this you can put

set -e -u

at the top of your shell script - it then ends with an error exit status when a command fails or an undefined variable is used.

Then you can call from the cron-job a wrapper script that calls the main script like this

sh -x main_script.sh || echo Failed with exit status: $?

With -x every line is printed out before it is executed. The output is mailed by the cron daemon to you.

You can also use a temp file when the output is too big:

sh -x main_script.sh > $TEMPFILE 2>&1
if [ $? -ne 0 ]; then echo Failed with exit status $? - see $TEMPFILE; fi

In case the exit status is > 128 the command was interrupted by a signal - e.g. someone 'killed' it, a segmentation fault occured or there was a out-of-memory situtation (how to get the signal from the exit status).

Specifying a username like mylogin is for the /etc/crontab file. With your command sudo crontab -e you are actually editing /var/spool/cron/crontabs/root and you should not specify a username in such a file, only in /etc/crontab.

If you have to run the command as user mylogin you have to put the line in /etc/crontab (and edit this with root privileges), or just put it in the mylogin user's crontab.

From man 5 crontab:

EXAMPLE SYSTEM CRON FILE
    The following lists the content of a regular system-wide crontab  file.
    Unlinke  a user's crontab, this file has the username field, as used by
    /etc/crontab.