Satriano: de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities. About degeneration for Artin stacks in char p.
A good introduction to the degeneration assuming liftability to can be found in Esnault-Viehweg: Lectures on vanishing theorems. In folder AG/Various
http://mathoverflow.net/questions/58834/degeneration-of-the-hodge-spectral-sequence
nLab page on Hodge-de Rham spectral sequence