1. I would think you could use more than 16t on each side of the channel to calculate properties. I would use the entire width of plate 20/6 = 3'-4".
I am not familiar with the terms Lp and Lr, but they must be similar to Lu in the Canadian code which is the length the channel can carry its full factored moment without additional bracing.
When pressure is on the plate side, the unbraced flange of the channel is in tension, so lateral bracing is not an issue. When pressure is on the channel side, the channel flange is unbraced except by its attachment to the plate which could be considerable. It might be prudent to add stiffeners on one side of the channel spaced at Lu. By so doing, I believe you could consider the compression flange braced.
2. I don't have AISC documents.
3. Similar to channel.
BA