compound that inhibits the activity of the key regulated enzyme in the pentose phosphate pathway

Answer 1

Short Answer: NADPH.

Long Answer: In this pathway, the rate-limiting enzyme (i.e. the slowest enzyme in the pathway) is Glucose-6-phosphate dehydrogenase. This enzyme converts glucose-6-phosphate to 8-phosphogluconolactone, and in the process it converts one NADP+ to NADPH. It is very typical in biochemistry, where an enzyme will be allosterically inhibited by it's downstream product, so that you don't overproduce a given product.