A basic diesel engine will inject a good bit before TDC. Diesel is quite slow to ignite, so to get peak power and good air/fuel mixing, the fuel has to be ignited long before TDC (IIRC at typical slow idle it's about 18deg BTDC). This is why diesels knock so much, as the engine is pretty much on the verge of stalling at TDC due to the high pressure.

With modern common rail systems, fuel injection is now a multi-stage process. As the piston approaches TDC, a small amount of fuel is pre-injected, which results in an intial flame, then as TDC is approached main injection occurs as a further series of injections, which ignite quicker due to the already burning fuel.



As for diesel 2strokes, they have existed in the past. Some had conventional valve trains, some were ported, but pretty much all of them were supercharged.