How much would you decide is the cost of a ring of fast healing (has a continuous cure light wounds spell)?
Is there something in the official rules to determine the cost?
Since the Forge Ring requires a 7th level caster, how many would this ring cure every round (1d8+5), assuming one does not wish to roll every round?
There's no real solid formula for this, regardless of what you're doing. Fast Healing is generally one, two, maybe three hit points per round, not a continuous 1d8+5 (average 9.5 hp per casting). Fast Healing 9.5 would be ludicrously expensive. Fast Healing 1 is complicated enough.
If I were making such an item I might do something where it only works up to 1/2 normal hit points. A
ring of desperation healing that grants Fast Healing 1 while its wearer is at or below one half of their normal hit point total and requires 24 hours to attune to its wearer might be reasonable to price somewhere around the 30,000gp mark. That's
totally ball-parking it. If it's priced much higher it wouldn't be purchased. (Who'd ever pay 100,000gp for a FH1 ring?) If it's priced lower it'd probably be a no-brainer item.
Try this for a formula. Price is 20,000gp + Fast Healing Granted squared * 10,000gp.
FH1 would be 20,000gp + 1^2 * 10,000 = 30,000gp
FH2 would be 20,000gp + 2^2 * 10,000 = 60,000gp
FH3 would be 20,000gp + 3^2 * 10,000gp = 110,000gp
Seems reasonable to me.