Q. Do I put Yes on claiming exempt federal tax holding?

A.  No.  But maybe. You are not exempt unless you had no tax liability last year and expect to have none this year.  Basically that means you expect to have less than $12,000 income for the year.

Q. Do I say Yes to Withholding exemption certificate from MARYLAND?

A. No.  Because you physically work in MD, you are subject to MD tax. That certificate is for residents of border states , e.g. VA

Q.  About Withholding exemption certificate from OHIO.  Yes or No?

A.  It's optional.  I would say yes.  You will have to file an OH return and will have a tax liability.  But, OH will give you a credit, or partial credit for what you pay MD. So, you will owe little or nothing to OH