rsync files across multiple user accounts

Is there a way to use rsync from the root account to access the directories and files of each user? I would only like to grab files in .csv format.

This command will backup everything in /home and save it to the remote host under /path/to/backup. It will retain users' ownerships and permissions provided the remote filesystem is capable of doing so

rsync -av /home remoteHost:/path/to/backup/

If you don't have root access on the remote system you should add the -M--fake-super option to backup file metadata (ownerships and permissions) in a way that doesn't need root access. Make sure that if you use this flag, you also use it for restores.

The second part of your question is a duplicate of Rsync filter: copying one pattern only. To limit the copy just to .csv files you can use this

rsync -av --prune-empty-dirs --include='*/' --include='*.csv' --exclude='*' /home remoteHost:/path/to/backup/

In general, yes. The problem you're going to run into is authentication. You can, for instance, run an rsync script from cron. Make yourself a shell script. If the source and destination are on the local computer, root works.

If the source or destination is remote, it's a much harder task. The easiest way is to bypass the issue --- use NFS to mount the remote disk on the local computer. You can also lookup ssh authentication... that's a rabbit hole for you to research

OK. Assume /root/backupuserlist is a list of users, one per line and /backupdrive is where you're backing them up.

#!/bin/bash
# backup /root/backupuserlist to /backupdrive

BK_USERS=`cat /root/backupuserlist`
BK_DRIVE=/backupdrive

for user in $BK_USERS; do
   rsync -av ~$user/ $BK_DRIVE/$user/
done

crate /root/backuserlist, and then run this as root... or put it in root's crontab or /etc/crontab ... you get the drift.