yes, the first two numbers (10/10) are the charges you have. The first number is how many is left, and the second is the number that item had when it was made. You cannot recharge an item, once it's charges are up, it's useless. However, if an item has 1/1 charges, that means it's infinite.
bascially the format is this: ChargesLeft/MaxCharges TimeUntilUse/[CooldownTimer, DelayAfterEquipping] so the ring in the picture above has a maximum of 10 charges, and hasn't been used yet (has all 10 left) It'll be ready to use in 30 seconds. Once used, it takes one full real life day until you can use it again, and you have to wait 30 seconds after you equip it before you can use it.