From what I'm reading you only add water to compensate for whats absorbed by the roots, and whats evaporated. And no to the nutrients, its just the water from the fish tank. The nutrients apparently would more then likely kill off the fish. To take it a step further, some people take the waste on the bottom of the tank when it builds up to high and raise worms in it, feed the worms to the fist, and use the casting for fertilizers for soil.
as an experiment, i've been running nutes in my aquaponic system for cloning/veg. TDS of my particular setup stabilized at around 300-500ppm (without nutes), depending on how hard i fed them. bumped it up to around 700ppm with some GH micro for about 6 months. i've even added great white a few times with no adverse effects. i swear superthrive made the fish bulk up in a growth spurt (probably due to B vitamins), or maybe i'm imagining it. small quantity of cloning/rooting also did no harm, although i don't even bother using it anymore because the system roots clones so well. adding all this stuff caused no harm to the fish or any major instability in TDS (which i assume means the ammonia-digesting bacteria didn't die) or pH or feeding/growth rate of fish.
i've been running my system at 1600ppm with cal-mag, silicate, and CNS17 bloom (still for just veg) for a few weeks. if fish don't die off in another 2 weeks, i'm going to try hooking up my aquaponic system to standard recirculating bubble buckets in flowering. my system is stocked 50 or so $0.17 feeder fish and have no intention of eating them. a handful of them died off in the first few weeks, but i also didn't properly cycle my tank. they could've been goners already: who knows. since i was only interested in a system that could be setup in a matter of days (not weeks, as is with a properly cycled tank), i skipped the cycling. i used an out-of-the-bottle bacteria to jumpstart tank cycling. maybe that helped. system pH super-stable at 5.9. also, i overfeed constantly. uneaten food gets digested in the biofilter.
the main advantage for aquaponic over traditional hydroponic is that you
DO NOT NEED TO MAINTAIN STERILE SOLUTION! that alone is worth investing $100 in a DIY setup and experimenting yourself for a few months until you've got it dialed in. my system has been running for 9 months and it really only seems to get better, even with adding all these nutes. no H2O2, no bennies (the solution is already full of them), and you get all kinds of nutrients and trace minerals that are in the fish food (eventually, fish poop).
yeah, i've thought about adding red compost worms and get all organic and shit, and i'm sure it would work well, but you know what? i'm not growing vegetables or fish that i intent to eat with this system. i don't even care about the nitrogen you get from the fish poop. (yes, you'd get nitrogen constantly, so for those of you that believe in the myth of depriving plants of nitrogen during flowering, this system is not for you, at least for flowering.) it's the massive bacteria population that makes it impossible for any root pathogens to colonize the solution/system that is the real reason to integrate aquaponics into your growing.
oh, and there is nothing to collect from the bottom since that all gets sucked up by the pump and trapped by the biofilter. anything not sucked up gets eaten up by the one algae-eater/bottom-feeder catfish-looking fish i have in there too. don't use goldfish. all but 1 of about 50 died.