Postmarked, but being so close to the deadline, I'd recommend hand delivering the form to the Election Commission office at the courthouse to eliminate any possible problems with mail delivery or delays.

From the Tennessee Division of Elections:

When May A Qualified Voter Register?

In order to participate in an election, a qualified voter must be properly registered no later than thirty (30) days before the election. The election commission office will process any by-mail voter registration form that has been postmarked at least thirty (30) days before the election. T.C.A 2-2-109.

Regarding the second question, if you have previously voted in Blount County you should not need to register again if you are still at the same address. If you have moved, you should notify the election commission of your new address so you can be assigned a new voting precinct and so you will show up on their rolls when you go to vote. If you have moved here from another county, you need to register in Blount County.

From the Tennessee Division of Elections:

Address Change Within County

To avoid complications on election day, registered voters should keep their local election commission informed of any change in address. To process a change of address, the election commission must receive written notification over the voter’s signature of such change, as late as five (5) days before the election. If on the day of voting the address on the voter’s permanent voter registration record differs from the voter’s current address, then the voter must complete an affidavit before being allowed to vote. The voter must vote at his or her new polling place or at a central location designated by the county election commission office.

To facilitate the process of keeping voter registration records accurate, the election commission conducts an address verification program to identify any voter whose address has changed but who failed to notify the commission. If the county election commission determines or suspects that the voter has changed addresses, the administrator of elections will mail a forwardable confirmation notice on which the voter may verify or correct the new address. If the voter fails to respond to the confirmation, and if the voter fails to otherwise update the election commission over a period of two (2) consecutive regular November elections following the date the notice was first sent, the voter’s registration will be purged. T.C.A. 2-2-106

Address Change To A Different County Within Tennessee

If a voter has moved to a different county within Tennessee , address changes are not considered updates. The voter is a new registrant in that county and must complete a voter registration application. The voter may either go in person to the local county election commission or mail the application to the local county election commission. All registration deadlines apply to new applications; therefore, the voter must register no later than thirty (30) days before the election. If the voter registers by mail, he/she must vote in person at the first election. This rule applies even if the voter has voted in the previous county where he/she was registered.

If a registered voter moves to a different county within 90 days of an election, the voter may leave his/her registration in the county where previously registered. The voter will have to vote in that county and at the correct polling place. Alternatively, the voter may choose to register in the new residential county prior to the registration deadline.

If a registered voter has been moved to a different county 91 days or more, the voter must register in the new county by the registration deadline. If this process is not completed, the voter will not be permitted to vote in any elections until after the voter has properly registered.