1) The term "decorrelation" generally accounts for processing that reduce autocorrelation within single, or cross-correlation within a grouupp of signals or images. Dooing that, it should preserve important features in the data.
2) In other terms, images often contains simpler "objects" (in terms of morphology: bumps, edges, textures) that are mixed, or distorted. Generally, unmixing them via decorrelation somehow simplify further processing.
3) Generally, yes, unless you have uncorrelated noise in your images. A classical and simple model is an order-one Markov or autoregressive process. Basically a pixel somehow depends (with a parameter $\rho$) on the past pixel, with uncertainty. If $\rho$ is close to $0$, you are already decorrelated. If $\rho$ is close to $1$ (typically $0.90-0.95$), the data is quite correlated.
The DCT was meant for diagonalizing the resulting autocovariance matrices with Toeplitz structure, to give fast estimates of their eigenvectors. Transforming a fat autocovariance matrix into a thin, close to a diagonal, matrix is an instance of decorrelation.