Is it permissible to remove the sticky liquid that appears after completing ritual purification (istinja') with stones (istijmar), in order to shorten the time and duration of istinja', and is the continuous application of water to the private parts harmful to health?

The fluid might be from the pure vaginal secretions that do not necessitate istinja (washing after excretion). Even if it were impure, performing istijmar (purification with dry materials) using three cleansing wipes or similar is sufficient for purification. You must avoid obsessive thoughts (waswas).