Before making an assessment of the problem yourself, but having armed yourself with the information posted here, perhaps you might consider getting an engineer to look the car over?
This may help you identify your particular model since it seems two were current in the year 2000:
http://en.wikipedia.org/wiki/BMW_3_Series
I've never heard of a BMW diff going [I don't drive one] and yours was the only hit I got on the first page by googling it as
00 BMW 316iSE differential
Googlong
BMW differential
got loads of results.
You might get better info amongst them but the following is for an earlier model and is writtne in American [foot-ponds, etc
]
http://www.bimmerdiy.com/diy/e36diffswap/
From the pics you'll see you need the use of a workshop a raised lifter for the car and proper tools.
For my money, before you start you should have done heavy work on cars before as there are techniques before you even approach the work.
You need to prepare - older models underbody work starts with pre-cleaning everything to get the light muck off and then careful work to remove corrosions and ease fasteners [nuts, bolts, clips] that may be rusted in place or siezed through electrolytic corrosion.
You'll need the help an experienced back street mechanic to do things in a way that won't result in a long replacement parts bill!
You will also need to bidget for the time to do this.
What may take a day on a recent model in good nick might take two or three days on an older model with siezed threads and rusted underbody sections.
Plus you'll need time to identify, remove and source replacements for any gaiters or seals you remove as they will probably not be re-usable.
Take heed of the disclaimer at the bottom of the page I or which I gave the link.
"Do this procedure at your own risk. Follow manufacturer's guidelines and specifications. If in doubt of your abilities, please leave this to a professional."
Remember that this is a critical component in your car, and any final assessment, assembly checking and preparation, and final placement work should be undertaken by an experienced mechanic, not you, particularly final fixing and pre-loading of bolts and nuts.
Ideally he should sign off on the work.
Let me put it like this.
I repaired my own bikes for years and kept them serviced.
I've helped people replace engines in cars.
I know a lot about guntering.
I wouldn'y touch diff work.
ONQ.