Hello,
Regarding the spheres model, for each sensor only one sphere is used for calculating the forward solution. So for all the dipoles, you're always using the same sphere for that sensor. So you can think of all dipoles as actually being inside all the spheres (the sphere radius does not matter in the calculation so you can conceptually make it as big as necessary to include all your sources). Now I'm not sure what you mean by "projected back onto the MRI".
For sLORETA, look for example at http://arxiv.org/pdf/0710.3341. The forward solution (lead field K) is size nChan x nSources. The main equation is: j = [(K'CK)^(-1/2) K'C]Phi. C = (KK'+aH)^+ here contains among other things the sensor noise (H) and has size nChan x nChan. In the main equation C is always multiplied by K, that's how you go from channel space to source space. Hopefully that helps you to answer your questions 1-3. For your question 2, the identity matrix would replace the sensor noise covariance H.
Cheers,
Marc