How are blacksmithing bonuses determined

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.

The formatting might still be improved, but here's the info dump for ya. These are from Pristine Quality shards.

Magic+Magic Sorcerer's Gem +1 all unlocked Sorcery skills

Magic+Lightning Gem of Abatement -20% Mana Cost

Magic+Fire Gem of Abatement -20% Mana Cost

Magic+Ice Gem of Abatement -20% Mana Cost

Magic+Physical Warrior's Gem +1 all unlocked Might skills

Magic+Protection Gem of Enlightenment +1 to all first four tier skills in all trees

Magic+Poison Rogue's Gem +1 all unlocked Finesse skills

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Lightning+Lightning Gem of Tempest's Vengence 75% chance to shock enemies when Attacked

Lightning+Ice Gem of Magic Resonance  +20% Lightning, Fire, and Ice damage

Lightning+Physical Gem of Opulence  +20% gold drops

Lightning+Fire Gem of Magic Resonance  +20% Lightning, Fire, and Ice damage

Lightning+Protection Gem of the Assiduous +8% more experience

Lightning+Poison Gem of Unrivaled Vitality  +50 HP and MP

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Ice+Ice Gem of Winter's Vengeance 75% chance to freeze enemies when Attacked

Ice+Physical Gem of Opulence  +20% gold drops

Ice+Fire Gem of Magic Resonance  +20% Lightning, Fire, and Ice damage

Ice+Protection Gem of the Assiduous +8% more experience

Ice+Poison Gem of Unrivaled Vitality  +50 HP and MP

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Physical+Physical Gem of the Subjugator +15% Damage and +10% damage resistance

Physical+Fire Gem of Opulence  +20% gold drops

Physical+Protection Gem of the Enlightened +10% experience

Physical+Poison Gem of Opulence  +20% gold drops

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Fire+Fire Gem of Summer's Vengeance 75% chance to burn enemies when Attacked

Fire+Protection Gem of the Assiduous +8% more experience

Fire+Poison Gem of Unrivaled Vitality  +50 HP and MP

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Protection+Protection Gem of Paralyzing Vengeance 60% chance to stun enemies when Attacked

Protection+Poison Gem of the Assiduous +8% more experience

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Poison+Poison Gem of Plague's Vengeance 75% chance to poison enemies when Attacked