I know damsels can get very aggressive and territorial, while pipefish need a much calmer tank, usually a species only. Has the damsel been picking on the pipefish at all?
Also I know they can be very picky eaters and usually do not take prepared food, eating only 'pods
' that require a well established tanks. I would definitely get some more live rock so he has more hidey holes to get away from the damsel.
As far as purple string algae, I assume u mean Cyanobacteria. That is usually caused by excess nutrients in the water like nitrates and phosphates. If u can lower these it should help and also cutting back on ur lighting will help also.