Enchanted Weapons: I notice that enchanted weapons have blue bars associated with them that deplete whenever I attack with said weapon. Does the enchant disappear once that blue bar becomes empty? If so, how can I re-fill the blue bar to keep the enchant from disappearing.

Amulets/Rings/Necklaces: I know i can equip these, however many of these accessories that I have are statless. And i just learned that I can add stats to them. But is there some special reason why (as an example) a statless Silver Amethyst Ring is worth more than a statless Silver Garnet Ring? If there is no reason, then I can sell the more expensive one without risk?

I'd like to know why you can only wear one ring when Oblivion you could wear two?

The enchantment never goes away on weapons, when its depleted it no longer works. Use filled soul gems to recharge your weapons. I believe price is only defined by the jewel in this case, the potency of the enchantment has to do with your skill in enchanting and the size of the soul used.

You're quite right in your first assumption that the blue line associated with some weapons is the "charge meter".

Enchanted weapons are recharged using soul gems which contain souls. You can buy them filled, or empty and fill them your self with the soul snatch spell.

Highlight the weapon in your inventory and press '
"T". You'll be shown a list of eligible should gems to use to charge the weapon.