Of course, different browsers ... different users ... all of this is relevant if and only if ...
you use a computer to which you and only you have exclusive access. Exclusive access is the ultimate control.
Absolutely.
Barring exclusive access to a system, exclusive access to the tools used is the next best thing.
For guys and gals who must surf at work what I recommend is either a personal laptop with tunneling software linked via encrypted tunnel to wi-fi or wired internet or a boot-able USB key-drive with tunneling software, a personal browser, and evidence/cleaner eradicator software.
You boot to the key-drive, if possible, use the encrypted tunneling software and personal browser and favorites on the key-drive, clean up using the cleaning software, leave no traces.
I.T. will be able to tell someone is on the internet at that node, but not what they are seeing. Even a packet sniffer will tell them nothing more than there is encrypted traffic going in and out through specific ports.
Now if the company has a written policy about encrypted traffic on their network... then you obviously can't use their network even in this manner. Most companies don't bother checking for encrypted traffic though [even though they should because it is a GREAT way to leak info and other acts of corporate espionage].