Deductions & credits

No, checking the box that states that you have foreign financial assets on Schedule B (I assume that's where you are seeing it) would not delay your tax refund. 

Have you checked Where's my refund website? Sometimes the IRS needs additional verification. Check the status of your refund there and follow any suggested steps. 

For state refund, use this Help Article.

Going back to foreign accounts. If the box that asks whether you are required to file FinCEN Form 114 is marked as yes (see screenshot), I would suggest taking a conservative stance and filing an amendment tax return unchecking any unrelated boxes. The penalties for not filing required foreign account forms are very steep.