Kingdoms of Amalur: Reckoning demo restrictions

Yes, you get critical hits with Staves (and Scepters and Chakrams) as a Mage and gems, DIY sagecraft builds or other Crit bonuses will increase the Damage and/or Frequency of critical hits.

Generally speaking, esp. with Staves/Scepters, you will NOT get physical bonuses. You WILL get physical bonuses with Chakrams, my work-a-day Mage Weapon.

Piercing, Bleeding bonuses are a no-go for most Mage-specific weapons as well.

Keep in mind that as opposed instead of a Finesse-type or Might-type character your Sorcery-type character will be inflicting (most) critical hits with Magic. So be on the look out for items that give you a "X% Critical Hit Damage with Magic" or just plain "X% Chance to Critical"

But you will do better with a Stave if you focus on technique instead hoping for criticals during 'button mashing.' The Stave is best as a slow masher: When attacking a single big baddie it's better to pause between button hits. HIT-breathe-HIT-breathe-HIT-breathe and then a quick bam-bam-bam with your melee weapon of choice. After all, the Stave is to the mage as the greatsword and hammer are to the Tank. It's for finish work and one-on-one fights -- not thinning the ranks. You'll want chakrams and advanced spells (lightning storm) for that.

10% damage affects all damage you deal, from the hit of your sword to its poison enchantment to the Shock spell (if you still have it).

10% Physical damage only applies to the base damage of your weapons, any enchantments that say Physical on them and Physical spells such as Quake. This does not include Bleeding damage, which has its own bonus damage category.

10% Bleeding damage only affects bleeding damage you deal, fire only affects fire, etc... you have to deal some in order for a % bonus to help you at all.

10% elemental damage is the only one I'm not sure about. I would suspect that Elemental damage simply means "everything that's not physical". It might only mean "fire, ice, and lightning", but leave out unusual damage types such as Poison.