Hi Erik. Since that was our kit I'm happy to jump in and help.
There are a lot of reasons why your system might be taking a long time to cycle. I actually wrote a blog post about this a couple months ago titled " The Top 10 Reasons Why Your System isn't Cycling". You might want to read through that and see if any of them apply to your setup. Cool water is definitely one that will slow the whole process down, for sure. If your questions aren't answered please feel free to give me a call at The Aquaponic Source as well and we can go through it interactively.
As for the seaweed not dissipating, that is a new one on me. Is your system running so that the water is circulating through the grow media? How much water do you have in your system? It may just be more concentrated than we usually see.
Please see this link to make sure all the bases are covered and at the same time find answers for yourself.
Your setup is OK for cycling but Sylvia was right to point out the temperature factor. Cycling requires consistent higher temperatures to coax the bacteria into establishing themselves and expanding their numbers. Cycling is a very delicate process and needs a lot of patience and in your case a little more than normal patience
No the seaweed will not harm the fish, but i do hope you're not planning on putting fish in your AP as it is not cycled as yet.
Ammonia is introduced at the start of cycling. Given the ideal conditions, bacteria will occupy the AP and multiply. Eventually the ammonia is suddenly converted to Nitrites and they peak before dropping off, this is called a Nitrite spike, shortly after this phase your AP will be fully cycled. That Nitrite spike is very harmful and hurtful to fish and damage their organs sometime beyond repair. The ones that may survive, by all commonsense should be living a painful existence. Its always a choice of the operator, but introducing fish now will not make any difference in the cycling process, it will not hurry things along in any way given your cycling limiting factors.
Its coming from the excellent minerals of the seaweed extract. To get some clarity can you post some more information of your setup, ammonia, nitrites, nitrates,temps......as we go along from here? You can use the search bar in the forums for topics on seaweed or read here http://community.theaquaponicsource.com/forum/topics/making-your-ow...