If you're training range, you may want to use an amulet of Power if you're in f2p, or judging by your stats you're p2p and you should use an amulet of glory. But yes, the amulet's effects are only active when you are wearing it.
Accuracy should improve as you level, but not after you've gained a 99 stat. The only thing the exp is good for after level 99 is gaining overall exp, or increasing your rank in that skill.
HP is exactly as colinsoccer said. It determines your combat level, and how much damage you can take before you die. However, as with most skills, a higher HP will allow you to gain more of a boost from Saradomin Brews, and other HP boosting items. This is, of course, assuming the boost is a percent, and not a fixed number
anyways i am f2p since 10 dec...