For a 20 gallon I think the minimum you would want for lighting would be 40 watts, I keep corals in mine with 130 watts and I would like more light on it.
No matter what time of year it is you want a heater in there just to keep it stable. It may never come on during the day, but when night comes and the temperature drops the tank tank will most likely drop and you want no more than a 2 degree sway from day to night.
The tank could be cycling.
I wouldn't be surprised if your NH3
was high. From your description of the seaweed it sounds like it is dying or dead and rotting in the water. Also the sand and water right on the beach is full of polutants, less so if you go away from populated beaches but still poluted. When they collect ls
and natural seawater it's off shore to make sure no polutants.