That's not nerite eggs. Nerite eggs are lager and shaped like sesame seeds. I would think that's some kind of fungus.

I would go with the advice provided as you're more likely to have success.

A smaller one should be fine. Ideally these frogs should be kept in groups of 3-5 individuals if your tank is big enough.

As far as I can see that's his breeding tube so not a worry. But the spitting food and general thinness could mean an internal bacterial infection or internal parasites of some kind. I would try treating him with Esha 2000 or Myxazin and see if that helps. His hiding away may be down to being bullied by the other male.

No two cycles are the same, so I don't think you have much to worry about. I would back off on changing water so often, and only top the ammonia up when it's near 0.

Do you have actual test results please for ammonia, nitrite, nitrate and pH?

Equilibrium only raises gH, it does not raise kH so you need to be adding kH to the water either by changing to an all-in-one product like Aquadur or by also using Seachem Alkaline Buffer. You'll need to use it in every water change, and during cycling when you're not changing water will need to monitor the kH and add more buffer when kH drops due to the activity of the bacteria.

The RODI takes all minerals out of the water so kH/gH depends on what you are putting back in. What minerals are you using?

The problem is not with the tank, it's your lack of kH in the water. kH is essential to the cycling process and the bacteria you're trying to grow cannot function without it. Crushed coral is not an effective method of raising kH. It can help keep it stable, but where there is no kH it dissolves too slowly to have an effect.

You said you cycled the QT in a week. That's really very unlikely so can you run through what you did and what made you think it had cycled?

Check the kH of your tap water. If that is at 1 or under then you need to be adding minerals to your water to get the cycle going and to maintain it long term. JBL Aquadur is a good product that raises kH and gH, which is also likely to be low.

There's no need to remove the substrate.