1. $6K for a 240D manual W115 is a good budget. I think you can find a pretty decent car to $3k. I got mine for $1350 back in 2004 (in West Hollywood) but the engine was going and the body is fair but it ran and did it's job. Depending on your level of detail you can replace a fair amount of things and or things that need replacing for $3k. Lift the mats for rust, check the trunk, check the jack points, and pretty much all of the rubber. Vac pump, vaccum lines, etc. It all breaks at some point or another.
2. I haven't driven a gas model but the euro M110 does have more power than the US motor. Al on the Stroke8 forum has had quite a few /8 cars so check that out. They do burn more fuel than a diesel though so expect significantly less fuel economy.
3. I would go for a manual unless it's a 300D automatic which is still a 17-18 second to 60 when new. Driving in LA is scary as it is with the constant aggressiveness so 240D auto would be pushing it in terms of safety unless it's being driven in traffic (as there is most of the time). I loathe the signal metered inclined onramps with a short merge lane, it's the 240D's worst nightmare.
If you find a car and do need some help or want to do a PPI I can send you an excellent mechanic contact on Lincoln in Santa Monica.