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You are reading the manual, right? If so, the numbers separated by a fraction indicate the bonus at level 1/2/3 of that skill.
Initiative determines the order in which troops move during a round. That is, a creature with an initiative of 25 will move before a creature with an initiative of 20. If both creatures wait, they will move in reverse order (as in King's Bounty).
I don't quite understand this spell. It works worse than dispel, and it doesn't remove everything. Apparently, it only removes negative effects.
Yes, you need to carry it in the hero's inventory slots, not in the backpack.