#1: does it have heated seats? That means it MAY have had the winter package, which included an LSD (3.15). Sure way to tell: get under the car and look at the tag on the diff. If it has an "S" and the ratio stamped on it, it's an LSD.
#2: The E brake controls only the REAR brakes.
#3: maintenance first, THEN upgrades, grasshopper. Read the stickies at the top of the E36 forum page.