Would the accumulation of historical prices and quantities exchanged in the market establish a long-run supply curve? How would the historical relationship differ from how firms (and economists) envision today's long-run supply in the industry?
I'm inclined to answer no to the first part of the question. To derive the competitive industry's short-run supply curve you horizontally sum individual firms' supply curves. You cannot derive a competitive industry's long-run supply curve in this manner because in the long run firms enter or exit the industry in response to the economic profits being earned--because of this entry and exit we don't know which firms' supply curves to sum horizontally. Also, as an industry expands or contracts due to firm entry or exit, the prices that firms pay for their inputs may change.
I'm confused about the second question. It leads me to think that you perhaps could use the accumulation of historical prices and quantities to establish a long-run supply curve.
You are on the right track here. Don't let the second question confuse you, since it is just asking how the accumulation of historical prices ...
Use of historical prices and quantities to establish a LRSC.