Hi Younes:
The SVD indicates the conditioning of the lead field matrix: if the spectrum of singular values is very wide (smaller singular values being several orders fo magnitudes smaller than the largest ones), the matrix is said to be ill conditioned mathematically, which is always the case with MEG and EEG. Computing the SVD spectrum helps determining how much regularization to apply to produce a reasonable (stable) minimum norm estimate of source amplitudes.
I am not sure what you mean, sorry. The result of the MNE is the production of a matrix called the imaging kernel, which is nsources x nsensors. It is a regularized version of the inverse of the gain matrix. If you want to extract the ith source time series, just multiply the ith row of the imaging kernel with with the sensor data array.
Sorry again: I am not sure what you are referring to exactly here. Can you specify a bit more?