Chalice of the Void enters the battlefield with X charge counters on it.
Whenever a player casts a spell with converted mana cost equal to the number of charge counters on Chalice of the Void, counter that spell.
If I pay 2 for a Sol Ring, is the ring countered by Chalice or does it count as something that costs 2? Also, do time stamps matter?
The ring is not countered, as the
converted mana cost of the sol ring is still

Any additional cost listed in an object's rules text or imposed by an effect isn't part of the mana cost. (See rule 601, "Casting Spells.") Such costs are paid at the same time as the spell's other costs.
Also, with Thorn/Sphere in play, do you have to pay an extra one mana in addition to alternative casting costs, i.e., Daze, FoW, Dread Return's flashback?
Yes
The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be

. It can't be reduced to less than

. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes "locked in." If effects would change the total cost after this time, they have no effect.