1. If your pet can dual-wield, it should. Giving it a 2h will turn DW off. Generally you only give 2h weapons to low level pets that can't DW anyways.
2. Pets proc the same* as players. If they are of level, it's a go.
3. Pretty sure this is the same as on live, 30 minutes.
*They tend to proc more often as they run on the NPC table of cheating.
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