Sounds to me that it's a failing crankcase ventilation valve, leaks usually aren't a quart every 1000 miles. Also the common leak places are likely to leak onto hot areas and smell. When a CCV valve fails the car burns the oil and runs slightly more coarse because it causes the vacuum system to work improperly. It's a gradual transition and is pretty unnoticeable until you address the CCV failure and feel the difference.
Here's my quick diagnosis (and I've written this in a few places on this forum already)
1. Take out the dipstick, examine the bottom (usually plastic and colored red or orange) if it for black sludgy oil residue, this is a sign of a failed CCV.
2. While the engine is idling remove the oil fill cap and then put it back on, make sure it't tight. While you do this listen carefully for changes or surges in the engine idle pitch, especially when putting the cap back on. If there's no change in pitch then the vacuum system may be faulty and it's usually due to a CCV failure. You can also remove the dipstick and listen for a change in the engine pitch.
A mechanic with the proper tools would seal a hose on the dipstick tube with a pressure gauge on it and look for negative pressure, if there's no negative pressure, change the CCV, it's not a particularly fun job but it's a common problem on these engines.
2000 528i Sport Premium 5speed