It may be possible to claim a dependency exemption for a relative living in Mexico. While the niece cannot be a qualifying child because she does not live with you, the niece may be a qualifying relative. As long as she cannot be claimed as someone else’s dependent, then you can claim a dependency exemption (assuming all other dependency exemption requirements are met).
An employer reimbursement or allowance arrangement that requires you to adequately substantiate business expenses to your employer, and to return any excess reimbursement.