Rust-colored marks on 316 stainless steel are often caused by extraneous or "free" iron. This iron comes from external sources such as using carbon steel tools as a part of the finishing or repair process, air born particles, etc.  Free iron should be removed via a thorough cleaning and scrubbing with one of the methods/agents described in ASTM A380 "Cleaning, Descaling, and Passivation of Stainless Steel Parts, Equipment, and Systems." A thorough cleaning often requires both alkaline and acid cleaning steps since acids cannot remove grease, oil, etc. After cleaning, a free iron test, also described in ASTM A380, can be used to detect whether any free iron remains. For your process, another problem to avoid is the contamination of the dryer exterior with HCl salts such as the material you are drying. If these salts are permitted to get wet and then dry, it can result in the concentration of chlorides due to evaporation and eventually chloride attack. Careful attention to operational details can avoid this contamination or an external coating can be considered. The coating must be resistant to all chemicals and solvents present, the surface must be properly prepared and the coating applied according to the manufacturers instructions. Consult a coatings manufacturer for assistance in choosing an appropriate coating.

Regarding your second question, the problem of a peeling lining should be discussed with the lining applicator to help determine the cause. A lining that is peeling could be cause by many different things including chemical permeation of the lining itself, improper surface preparation, and improper application. A vendor specializing in the lining of chemical equipment should be consulted so an appropriate solution can be selected. Assuming proper surface preparation and application, many polymers including PTFE would have better chemical resistance than polystyrene.