That sounds much like a situation where you need a vet check.
Locking and popping could be arthritis while the back could be sore and explain his saddle shyness.
My best suggestion is don't ride him and call a vet.
you seem to have a compound question. I do not think that the feet dragging is in anyway related to the saddle shyness..the saddle shyness could be him anticipating the girth that will be tightened around his belly, and his flinching could be a response of that anticipation. The back fetlock popping and locking could be arthritis depending on age, breed and discipline. dragging the back feet could be his natural gait, an SI joint issue, or a suspensory ligament issue. if he's mostly sound but possibly stiff, then you can eliminate ligaments as a cause and focus on the hips (SI joint) and wether this is the result of underdeveloped (possibly atrophied) muscles. If its muscle underdevelopment (i.e. you can't find cause and it's his natural gait) you can focus on exercises that include cavaletti and potentially lunging a LARGE circle with a surcingle (pessoa would be best) to help build up his hindquarters.