The black and green particles...
Some time before you closed the intake seacock, some kind of animal or vegetable--most likely vegetable--sea life got sucked into the intake line to die and decay. Usually it gets into the channel in the rim of the bowl, but prob'ly in your pump too if you see 'em when pumping in the dry mode. The whole system needs to be very thoroughly flushed out.As for what stinks...urine can stink just as much as solid waste...it's organic matter too. So there's no reason to avoid flushing solid waste, 'cuz when ANY organic matter is left to sit in an anaerobic environment--which is the condition of the inside of the hoses--it generates gasses that stink. Which is why it's very important to rinse out the hoses with clean fresh water before the boat sits. Closing the seacock and flushing by pouring water into the bowl is not the best thing for the toilet pump...'cuz what's in the bowl only goes through the bottom of the pump...all the rubber parts at the top of the pump stay dry and therefore wear out faster. A very simple solution: tee the head intake line into the head sink drain line. Flush with sea water...it doesn't make a bit difference in the tank whether you flush with sea water or fresh, only in the hoses when the boat sits. To rinse all the sea water out of the system, close the sink drain seacock...fill the sink with clean fresh water...flush the toilet. It will pull the water out of the sink, rinsing all the sea water out of the whole system--head intake line, pump, channel in the rim of the bowl AND the discharge line.If you insist on flushing with fresh water all the time, keep the sink drain seacock closed...run water down the sink to flush the toilet. Or better yet, install a 5-6 gallon UNvented bladder...connect the fill to the sink drain line using a y-valve (since there's no way it can put the boat at risk, even a $3.95 garden hose wye will work for this application)...connect the head intake line to the bladder. No other plumbing needed. To fill the bladder, run water down the sink with the y-valve open to it. To use the sink, open the y-valve to let it drain out the thru-hull. You say you're new to marine toilets and tank maintenance...I suggest you check out the link below...it'll take to you a comprehensive "marine toilets and holding tanks 101" manual that should help you solve the problems you already have and prevent new ones. It also includes some tips that should make replacing hoses a bit easier and a LOT less disgusting.