I didnt read every response, but the short answers are:
1. Yes, a corroding magnet can poison your tank
(looks like another fine Two Little Fishies product killing coral, their magnet rusting issues are well known).
2. The difference between a magnet corroding/breaking down and GFO is that one is pure ferric oxide (GFO), but a magnet can contain all manner of metals that can be harmful to the tank, so when a magnet starts to corrode and break down, it can expose the tank to those metals.
I have spoken with Julian Sprung about the magnets and he maintains that it is not an issue, but they can not guarantee that their cheap magnets do not contain other metals, and as long as they refuse to pot the magnets in epoxy, they will corrode and be a risk to the tank.
The simple solution is to not leave your lettuce clip or nano-mag magnet in the tank all the time.
To recover, I'd run GFO, cuprisorb, and carbon, and do some water changes. Then be patient.
Oh and DONT run a ton of GFO or carbon all at once, it will drop your alkalinity and be a shock to your system inhabitants. This problem took a long time to get bad, and unfortunately it will take a long time to get better. patience.