With over 500 views and no right answers, here are the answers, which may surprise you.
I. Beech A23 MUSKETEER II introduced in 1964 model year.
2.A. All three trailing link landing gear are interchangeable.
2.B. The wing uses honeycomb ribs with bonded smooth airfoil aluminum skin without rivets.
2.C. An oddball Lycoming IO-346 fuel-injected four cylinder engine of 165 Hp at 2,700 rpm was used, derived from a six-cylinder Lycoming engine block. This problematic engine ran hot in the Beech installation, downing at least two MUSKEETER aircraft that I personally am aware of in SoCal in the late 1960s. To my knowledge, this engine never was used in any other production aircraft.
An alternate answer 2.C. could be that an entirely new plant was built in Liberal, Kansas by Beech that began manufacturing operations exclusively for the MUSKETEER series in June, 1964 for production of the Beech A23, A23A and A23-24 models.
Beech also offered an optional left side door in these models, in addition to the right side door, which was unusual for low priced four seat aircraft at the time. Because of the size, construction and usual Beech quality of these models, they were heavier than comparably powered Piper low-wing Cherokee series aircraft and were not good performing aircraft with four seats occupied. The optional dummy practice landing gear lever of the quiz question was probably not often selected for installation.
Incidentally, I met John Elliott, Beech's chief project engineer on the Model 23 MUSKETEER series in the Summer of 1966 in Minnesota at Lake Elmo Airport during a Sunday demonstration sales trip of his. He subsequently left Beech and formed Elliott Aviation. I had flown over in a Piper Cherokee from Anoka County Airport.
3. Bonus answer. The Beech MUSKETEER series evolved into retractable gear models and the Beech SIERRA of the MUSKETEER series spawned the Beech model 76 DUCHESS twin engine trainer that used a SIERRA fuselage, bonded honeycomb wings and shared structural components. The Model 76 DUCHESS heralded a new class of light twin engine trainers including the Grumman/Gulfstream American GA-7 COUGAR and Piper PA-44 SEMINOLE.
The Duchesses were also built at Beech's Liberal, Kansas facility because of the common technology.
The MUSKETEER line introduced bonded honeycomb rib rivetless wing construction to light aircraft from Beech's experience building truss-grid honeycomb core material control surfaces for the Convair F-106 jet fighter.