Getting the Most out of Springs

"Springs should curve gently like a the shape of a feather (My image)."
I like them to be straight when the key is at rest. Largely aesthetic. This means that when the spring is out of the cradle, it needs more curve at the 'post end than the other end.

The spring should be bent a little further than you might think necessary as it is fairly easy to bend it back a little if necessary when the horn is put together. "
I'd replace the first word 'bent' with 'pre-tensioned', to avoid ambiguity.

"Add a drop of oil to the cradle"

If there is a rolling action of the spring in the cradle, then it is hardly necessary. However it will reduce sluggishness if there is a sliding action between the metals in the cradle. It is to do with spring diameter and cradle design, and the geometry of the area.

"Spring can be burnished to revive them."

That needs context. Does the burnishing refer to making the surface smoother, or to work hardening a non-steel spring material, say copper alloy silver or gold? (The latter should be necessary only if the spring has been over-heated; these metals do not go limp with use. Nor does steel.) When you refer to the writings of Thorp, perhaps you should give page number and paragraph.

No.. But putting a curve in it is what puts sufficient 'pre-tension' in the spring. If that were not there, then the spring would not be strong enough to do its job.

If you put a sharp bend in the spring, near the post, the spring may break more easily, or even break while being bent, but it would otherwise function the same as if it had a curve. It would LOOK amateur.

However, looking at the tiny detail... Where the spring contacts the spring cradle, the spring should be parallel with the axis of the hinge, and the mounting of the spring should be collinear with that section of spring.

Otherwise there is a rubbing action (in the direction towards and away from the spring's mounting) rather than a minute rolling action when the spring cradle rotates around the hinge axis during use. Any rubbing action involves more friction than a rolling action.

In practice, this issue is just fine on most saxes.

However a similar issue involving the way flat springs rub along the body when the key is moved, is a significant friction issue on many saxes. Usually a little lubricant is an effective band-aid, and should really be there anyway.