good diyer job
Purpose of the diff. fluid or the differential? Purpose of the fluid is to keep those differential gears lubed.
You more than likely will not see any difference after you replace the fluid. 60k sounds about right. Use a lubricate rated for "gear lube". Based on the type (if it is synthetic it will cover multiple weights) it should go up to 90 weight. I purchase mine local from an advanced type of place. These places will have quite a selection.
You have to raise the rear of the car and make sure it is safe to climb under there (always do this first). Next remove the fill plug (14mm is right) all the way. I would recommend having a 1/2" drive 14mm allen socket to put on a breaker bar to remove them. Put your catch pan underneath the diff. and remove the drain plug. Try to have it hot when you do it. Reinstall the drain plug, fill until it runs out and reinstall the fill plug and you should be good to go.