Dick, get The Art and Science of Sails by Tom Whidden and Michael Levitt. It is relatively modern and answers many of your questions.And has a bibliography with much more reading material including books and articles.
Interesting that in the 1983 America’s Cup where everybody thought Australia Two was terrific for using a winged keel it should also be remembered for its outstanding vertical cut warp oriented kevlar/mylar sails that Whidden says were “a consequential part of the entire effort”.
Unfortunately, this book will cost money and I know you find that offensive but you really should break down and BUY it…
Doug eluded to the fact that sail cut is often more related to strength than shape.
Sail shape is easy to measure and quantify and there are plenty of ways to stitch pannels together to achieve that shape. However, the load carrying ability of the cloth, and the resulting weight of cloth required to achieve a given life objective is really what drives sail cutting. The pinnacle of this technology (as of a few years ago) was North’s 3DL technology where fibers of aramid (kevlar) and carbon are laid between two continuous sheets of mylar while on a mold. This results in no seams, no pannels and fibers oriented in the directions needed to maximize the strength of the sail for a minimum weight.
As far as loose footed mains goes, take a look at Endeavor’s main. They used sliding tracks on their “boardwalk” boom to allow the foot of their sail to slide from side to side. They even used stoppers on the track to set the camber of the foot of the sail. If the trimmer wanted more camber, he would have a crewman walk along the boom and set the stoppers a bit further out. Brilliant!