Jenkins Slave Permission Denied while copying slave.jar
It looks like the problem is tied to your Remote root directory setting. That needs to be the location of the slave.jar, as Jenkins will try to execute it from there.
As for the permissions, the Remote Root Directory (whatever you set it to) needs to be configured to allow Jenkins to access it.
Therefore, if you change your Remote root directory setting to be /var/jenkins/ in your case, it should launch the Jenkins slave successfully.