An iPad can be backed up over WiFi with iTunes or you can plug into your computer and use iTunes to backup that way. You can only backup your iPad wirelessly to your own computer if you are on the same WiFi network. So you cannot remotely backup your iPad to your home computer from work. You have to be on your home wiFi network to backup via WiFi to your computer.
However, you can also backup your iPad via WiFi using iCloud, if you have iCloud setup on your iPad and you can do this anywhere that you are connected to the Internet via WiFi.
In both cases the iPad can be setup to backup automatically if the device is plugged into power, the device is locked (asleep) and you are connected to WiFi.
This might help you understand the process a little better.
How to backup and restore from a backup
http://support.apple.com/kb/HT1766
As long as you are using private browsing nobody should be able to track your Internet usage from the device itself. There are always ways to track what someone is doing over the Internet if you have the knowledge and the wherewithal to do so but that would occur from the ISP and not the device itself.
But keep in mind that if your are doing something on the Internet that you feel that uncomfortable doing, then you probably shouldn't be doing it. If you have concerns about your browsing usage you might want to consider talking to your employer as well, since after all, it is their iPad.
But if you use private browsing, there should be no evidence of your browsing history on the device that can be accessed by anyone from the device itself. Your employer cannot access your history remotely on the device itself.
