Usually the tax benefit on the state level is a state income tax deduction. I just looked it up, and Tennessee doesn't have a state income tax, so that is why there are no state income tax deductions for making 529 contributions to the Tennessee plan.
Yes, all 529 plans receive the federal tax benefits - there is no federal deduction for contributions, but earnings grow tax-deferred, and distributions that are used for qualified educational expenses are tax-free.
You can use the funds from a 529 for any qualifying higher education institution anywhere, regardless of the state that sponsored the particular plan. It can be anywhere in the US, and IIRC even a few foreign schools qualify. Pretty much any school that offers federal student aid qualifies, which includes pretty much all US universities and colleges.