Quantum capacity for ensemble of Pauli channels
For your question (1), the answer is yes. The 'hashing construction' for quantum encoding is independent of the quantum channel you use, so if you use this construction for encoding, you can send information over an ensemble of Pauli channels at the right rate. (Actually, this is slightly incorrect ... you do need that the input state you use in the formula for coherent information is the same for all the channels, but in the construction discussed by Preskill it is.)

The original paper Shor and Smolin does not mention an ensemble of channels. If you take a depolarizing channel near the quantum-capacity threshold you can achieve a larger quantum capacity by considering a new superchannel where one signal of the superchannel is five consecutive uses of the original channel. When you apply the 'hashing bound' to this superchannel (acting on a 32-dimensional quantum space rather than a 2-dimensional one), you find that the formula for quantum capacity is larger than five times the formula for the original channel. There is only one channel being considered here: the superchannel composed of five uses of the original channel, and not an ensemble of channels. The ensemble of channels comes in when Preskill gives the intuition for what is happening in Shor-Smolin.

(And of course you should replace five in the above paragraph with the appropriate value of $m$, which is only five for some of these constructions.)