You need to provide specific models, core 2 duo is not specific at all, there is a very large range, and quad core is even less specific ranging from an Athlon II X4 620 up to an i7 2600K, unless you meant core 2 quad in which case you still have a range from Q6400 to QX9775
A slow quad will get beaten by a fast dual core in some things, a fast quad will usually beat a dual core, but if you are looking at two that are similar in speed, but different in price it really depends what games you are using as to which one will help more, like GTA IV really needs a quad to perform decently, but there are many things that a fast dual core is better in.
The more information you provide the clearer the answers can be.
Thats an impossible statement and doesnt contain enough conditions, if we average all games together and average all core2duos together and average all core2quads together, you get a meaningless blob of data that doesnt tell you much since nothing is ever average, RTS games and FPS games like different things in CPUs.
The average core 2 duo is clocked higher than the average core2quad but rarely will you get the middle of the road unit.
For years people have been saying that games will be taking advantage of quad cores more, its a very slow increase, and you will end up upgrading before even half the games on the market use 4 cores.
Give specifics, which core 2 duos are you considering and which core 2 quads are you considering, you cannot take broad generalizations because in computing everything is situationally dependent.