1) In an engineering context efficiency has a very specific meaning ie it is the ratio between the energy you put into a system and the useful work that you get out. In itself this doesn't tell you very much about the amount of pollution produced in the process.
Fuel economy is a bit different as it considers the overall energy(fuel) use of the car as a whole system and while engine efficiency is part of this the mass and drag of the vehicle are equally important.
Pollution emissions is more closely related to fuel economy than efficiency but even then they are not identical. Clearly all else being equal if you burn more fuel you produce more emissions and equally an efficient engine is not necessarily clean, indeed there can be situations where emissions and efficiency are in conflict (especially in the case of NOx emissions).
2 & 3) Fuel economy is the main selling point for diesel engines. Even if the fuel is not cheaper per litre (in fact it has been substantially more expensive than gasoline in the recent past) the overall savings in fuel uses can be significant, especially for high mileage users. In very general terms diesel engines provide more low rev torque and are more robust and durable
4) Diesel engines tend to produce more emissions which are immediately dangerous to humans, although this tends to be a local problem first and foremost, particularity in urban areas.
5) It depends, carbon dioxide is an asphyxiatiant in large enough concentrations but not actually toxic per-se, carbon monoxide is (sort of) toxic in that it binds to haemoglobin and can cause asphyxiation although this is only a real problem in moderate concentrations in enclosed spaces rather than being a long term cumulative toxin. 479
Actually one of the biggest concerns with diesel is particulates especially nano-scale carbon particles (soot) which can accumulate in the lungs with the problems associated with any fine particle inhalation and may also be small enough to cross biological membranes.
6) In some cases reducing NOx emissions can be in direct conflict with efficiency as they are produced more readily in lean-burning, high compression conditions which are preferred for efficiency. There is also the fact that catalytic converters (which are intended, among other things, to Reduce NOx emissions) require fairly specific exhaust conditions to work properly and can be damaged and clogged by the particulates in diesel emissions. There are also diesel particulate filters but these are themselves fraught with engineering challenges and, in particular, tend not to work well in the low mileage, low speed conditions encountered in urban driving where particulate emissions are the biggest problem.
Having said all of this there is a difference between the health effects of local pollution and the global effects of more persistent emissions. CO2 and its effect as a greenhouse gas is the obvious one but there are also more general effects from petroleum extraction, handling and processing to consider.
Equally you can also look at the dangers inherent in the fuel itself. Gasoline is certainly more dangerous to store and handle and being more volatile can contribute to atmospheric pollution just by evaporating.
Yet another complication is that many fuels now have at least some bio-fuel component ethanol for gasoline and vegetable oils for diesel.
Also in this context technology is changing rapidly in response to consumer demand and government regulation so there is always a danger of comparing apples and oranges eg a 2 to 5 litre truck engine is a very different thing from a 1.2 litre hatchback regardless of petrol vs diesel. 479