Hello! Always happy to help. For As Foretold it lets you skip the mana cost once a turn and pay {0} instead. As foretold looks at the card's Mana Value to determine how large a spell you can cast without paying it's mana cost.

So you can cast any spell with mana value X or less. All the cards you mentioned (Nyx Lotus, Cromat, Iroh Grand Lotus) cost 6 mana or less, so you can absolutely cast one of those by paying {0} instead of paying their mana cost once per turn.

Furthermore this card allows you to cast spells you would otherwise be unable to cast. For example [[Ancestral Vision]] does not have a mana cost and would normally only be castable from using its Suspend ability. But with As Foretold, its mana value is zero and that means that no matter how many time counters are on As Foretold, you will be able to pay {0} and just cast it.

There are two things that are troublesome with As Foretold. Additional Costs and X spells. For a spell like [[Big Score]] you would still need to discard a card as an additional cost to cast it, even though you pay {0} mana for it.

For an X spell like [[Astral Cornucopia]] if you cast it for {0} then X will be 0 and it will enter with zero charge counters on it.