Is an autopilot rudder channel available on B737? None I've flown. Every QRH I've seen B733/737/738 has instructed A/T off with SE ops. True, if an engine fails in CRZ the A/T will increase and try to maintain speed. I'm not sure how long it will remain connected. On takeoff it will disconnect during climb out.
Yes, the Rockwell-Collins autoflight system (new MCP with the slightly larger buttons) on the 737NG has a rudder channel. You need to order the rudder servo as a customer option though. It is needed to use the CAT IIIb fail operational mode including automatic rollout and OEI CAT IIIa capability. We fly 737s equipped that way for around 10 years now.
Question to the AB pilots: when flying an approach with A/T engaged do you follow through on the T/L's? If not where do you have your inside hand? I suspect the B777 Asiana PF had both hands on the yoke; might be wrong.
I guess it depends on your SOPs. As part of our general SOPs for all fleets we have to "guard" (have the hand on them) the controls below FL150 with the autopilot engaged. Thrust levers have to be "guarded" latest below 1000ft, but it is advised to have the inside hand there below 5000 ft. So yes, we "follow through" (not that anything is moving) on the thrust levers on the airbus.