3 green’s
1. Yaw is angular motion about the vertical axis, you stop yaw by use of rudder. The string is an indication of the relative airflow in the lateral plane (sideways); the angle between the string and the aircraft longitudinal axis is known Beta. This is the equivalent of Alpha in the pitch plane.
2. For maximum rate of climb fly the aircraft as recommended by the manufacturer (normally V2), there should be no difference in flying technique between straight and turning flight. Be aware of bank limitations as the engine out climb speeds are usually slower than normal, thus there is a reduced margin from stall. Flying the correct speed is also important for maintaining control of the aircraft.
3. With wings level and steady heading there should not be any yaw.
In a turn there is a component of ‘yaw’, the nose moves round the horison. If there is a small beta angle then rudder may be required. Many variations in this area depend on the aircraft type, auto stabilization, etc, etc.
4. Generally yes, but there are always exceptions. Some aircraft with roll spoilers etc accept small side slip angles (beta) and climb with less than optimum wing down or even with wings level. This option may require a slightly higher speed than theory predicts, but with no need for roll control input, the spoilers remain in which gives lower drag and easier handling.
5. Still looking for an appropriate heavy weight book, but meanwhile try FAA-H-8083-3 - AIRPLANE FLYING HANDBOOK chapt 14, not much, but a start.
http://pages.prodigy.net/jedinein/acs/faappselbook.html