Well, looks like I can take up this job.
1) Most importantly, get this straight, you can fit whichever nikkor lens on to any nikkor camera. (Actually got a handful exceptions, but those are not the common lenses people will use. Highly unlikely you'll come into them)
2) What is DX format? DX means the sensor in the cam is slightly smaller than the size of a film frame (36mm X 24mm). There are full frame cams, represented by FX format, e.g. D3, D700. Their sensor is full size 36mm X 24mm. In the case of DX sensor, it is roughly 23.7mm X 15.7mm which is about 2/3 the size of full frame. With the exception of D3, D700 and film SLRs, the rest dslrs are in DX format.
3) Is DX format only adopted by Nikon? No. Although DX is a name used only by Nikon, we usually call these smaller digital sensors as cropped sensors. Most cameras out there, from canon, pentax, sony you name it.. they produce mainly cameras with cropped sensors. If you want a full frame dslr, they are the expensive ones e.g. canon 5D, 5D MkII, 1Ds MkIII, Sony A900 etc. With the exception of Olympus, it uses Four-Thirds system (4/3). Their sensor is in a totally different height:width ratio of 4:3. The rest (Nikon, canon, sony...) uses 3:2 ratio.
4) Is DX format a problem? Not really. Or else why so many ppl still using cams with cropped sensor? The difference it makes, is the viewing angle becomes smaller at every focal length. For nikon DX sensors, say you shot at 20mm, the viewing angle will be similar to (20X1.5)mm in a FX camera. You should the longer the focal length, the smaller the viewing angle.
5) What is AF, AF-S? AF-S
is a type of lens that has an in-built motor to do the focusing. Usually because of the in-built motor, focusing can be faster than AF lenses. D40/D40x/D60 do not have a mechanical focusing drive in the body. D90 has. If you put an AF lens onto D40/D40x/D60, it is perfectly fine, but AutoFocus will not be supported, because there is no motor to drive the focusing. You must ManualFocus even with an AF lens. That is why AF-S lenses are prefered for D40/D40x/D60, because it will then have AF function. D90 has the mechanical drive in the body, so if you mount AF lens on to it, you can AF.