API's ammonia test is a salicylate reagent based test so the Amquel is not the culprit. You do have an ammonia spike. Your flow is ok. You should look into the maxi-jet mods to increase, as well as spread the flow out. Eventually, your going to want some different pumps for circulation. Even with the best pumps, with the best controllers, aquarium will have dead spots(areas where detritus accumulates). Turkey basters are great for getting this up into the water column to be filtered out. Do this 30-60 minutes before cleaning your filters.
I couldn't find out for sure, but Foster's premium carbon is likely a bituminous carbon. Lignite carbons are typically a little better. A great source for carbon is bulkreefsupply(BRS). They sell both varieties as well as one called ROX. I would not recommend the ROX carbon at this time for you. It's so strong, used improperly, it will cause even more problems. Even many 'experts' have problems using it. A reactor is the best way to use carbon, although a bag will work(takes twice as much).
I've never used Seagel or any aluminum-based phosphate remover, but there are many cautionary tales out there about it. Most people use GFO. BRS sells this too, in two varieties, normal and high-capacity(HC). I would recommend the normal for you at this point. The HC is very strong, and like the ROX, used incorrectly will cause more problems. Again, a reactor is best. All that said, be careful using a phosphate remover without a decent/good phosphate test/meter. You can easily starve your corals. A word of caution, generally it recommended to use half of the about of GFO that BRS recommends. If you go that route, just ask, we'll help you out.
In general, most general aquarium-use RO/DI filters are pretty much the same. There are some out there with cool features, but a standard model is all you should need. Once again, BRS is a great source. I use their 5-stage plus at home. It has the backflush setup on it, great for preserving the RO membrane. The standard 4 or 5 stage RO/DI would work fine though.
Some good carbon and the RO/DI unit will help you the most, so start out there.
BTW, I have no affiliation with BRS, other than I personally use their products and sell/recommend them at my store. They have great customer service, quality products, and good pricing. Many local reef stores will carry their products or you can buy them online. They also have great videos online showing how to best use their products.
