You did not mix the salt first? This is generally not a good practice. It is ok for a new build, but once you have stock in the tank you MUST mix the SW before putting it in the tank.
Where are the leaks? Is it cracked or damaged pipes? A leaking bulkhead? Teflon Tape (plumbers tape) is a simple and effective remedy for many leaking joints.
Have you filled the system to capacity? If so, I would drain a portion of it and mix the salt in an outside container. I would mix it VERY strong and then refill the tank. Test salinity and then adjust. I just don't trust that all of the salt will dissolve properly in the tank itself.
Think of it like this... You can mix a batch of saltwater to say 4x the normal level using the water in the tank now... once you add it back, it will dilute in the fresh water you have in the tank... then check the salinity... If its low, repeat the process... if high, drain a bit and add fresh water.
Not quite true. The water will stagnate if it is not moving. Since you already have it in the display with the sand, it will go off faster. You should have a way to keep the water moving and break surface tension to avoid stagnation.
As for dipping the towel into it, no worries there.