Yes, on all counts, assuming there are no state prohibitions on such a fee.
As a different example, a bank can offer an MMDA without allowing check payments at all. That makes it a lot like a savings account, but they're both covered in the same regulatory description in Regulation D, anyhow.
Just be sure that you don't rely on your more restrictive limits and fee to protect your bank from Reg. D problems. If you mistakenly let a customer go over the Reg. D limits, and don't take appropriate action, you could be criticized.
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John S. Burnett
BankersOnline.com
Fighting for Compliance since 1976
Bankers' Threads User #8