Are Fulbright monthly stipend payments taxable?

Yes, usually that is not used for education expenses and is taxable. 

Is the stipend reported on a tax form?

If not, you can enter it as additional scholarship not already listed on a tax form in the education section when you enter the 1098-T.

If the 1098-T is not being entered on the student's return, go to that section 

Deductions & Credits

Education

Expenses and Scholarships (Form 1098-T)   START or UPDATE

Enter as if you are going to enter the 1098-T, say no, you don't have one, say yes, you have an exception, (Don't enter Boxes) until you finally get to a screen that lets you enter additional scholarship. 

Enter the stipend there. 

It will be reported on Schedule 1 line 8r.