In the pH system of acids and bases, are there 10^-7 loose ions per liter (at pH of 7) or per mole of solvent? (Or per mole of total substance?)
In the pH system of acids and bases, are there 10^-7 loose ions per
liter (at pH of 7) or per mole of solvent? (Or per mole of total
substance?)

In a rigorous sense none of the options is correct, because pH being approximated by molarity is an approximation itself. The problem lies in the measurement itself and pH should be
$$pH= -log (a_{H^+})$$
The pH probe &quot;senses&quot; the activity of hydrogen ions not the molarity. This is why the pH of 5 M HCl is not equal to $$pH= -log (5)$$
There are no free or loose hydrogen ions in water, like a bare proton, rather this proton is attached to a network of water molecules.
Wiki is talking about an approximation. 1 ton is equal 1000,000 grams, so 10$^7$ mole/g x 18 g $\ce{H2O}$ is indeed 180 t. This part is correct so far. Note the author must be following metric ton. The whole world does not follow the US ton.
1 liter of water weighs ~ 1000 grams. Then 1000 g water contains 10$^{-7}$ moles of $\ce{H+}$, and 18x10$^{7}$ g water should have 1.8 x 10$^{-2}$ mol $\ce{H+}$ or 0.018 g $\ce{H+}$. I don't get 1 g.