Yes, if the L-2 extension was also approved.
Your dependent will file the I-765 for themselves.
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If the L2 is in status, then the L2 can apply for an EAD.
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What's in the passport isn't important .. the I-94 controls.
Yes, if the I-94 is still valid, then the dependent can file for an EAD .... they take about 90 days.
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Yes, if the L2 has been extended also and if the dependent has remaining validity on the L2, your spouse will be approved through the ending validity of the L2. Make certain you include proof that you have maintained your L2 status. (pay slips, W2, etc..)