If tuition reimbursement is provided for Fall 2017 but is paid on 1st check in 2018. Do I enter this information on my 2017 taxes? I don't want to claim the income twice (2017 & 2018)
Yes. You will include the tuition reimbursement on you 2017 tax return. What really matters is that you did not pay the tuition. It does not matter when you were reimbursed.
If your employer reimbursed your tuition expenses, and the reimbursement was not taxed or included on your Form W-2, then you are not eligible for education credits. Education credits are available for taxpayers who pay for qualifying education expenses.