The charges you discuss would almost surely be brought in federal court, rather than in state court. This would probably mean a trial in one of the U.S. District Courts in Tennessee while being held in a country jail pursuant to a contract with the local jail from the federal government.
Upon conviction, the individual would be sent, in all likelihood, to the United States Penitentiary which contains federal death row in Terre Haute, Indiana.
While incarcerated in Terre Haute, any direct appeal would be handled by the U.S. Court of Appeals for the 6th Circuit, which includes Tennessee, but habeas corpus petitions would be brought in the U.S. District Court for the appropriate district in Indiana that includes Terre Haute, and subject to review by the U.S. Court of Appeals for the 7th Circuit.
In principle, the federal appellate process for death penalty cases is quicker. One direct appeal to the U.S. Court of Appeals (with possible prompt en banc review of that decision), certiorari to the U.S. Supreme Court from there, and a collateral attack by way of writ of habeas corpus, first in the U.S. District Court of the place of incarceration, then to the U.S. Court of Appeals for that jurisdiction (with possible en banc review) and then certiorari to the U.S. Supreme Court. It is conceivable that this could take as little as five or six years.
But that doesn't mean that an execution would happen swiftly. The federal government has executed more people this summer than it has in more than five decades, in part, because the current administration has been determined, more or less from the early days of the current Presidential term, to push to have executions of convicted people on death row carried out, while previous administrations have not necessarily been so determined to press forward. Because the federal government rarely carries out executions, there is a lot of "red tape" and litigation involved in getting the execution process and protocols in place and approved.
In contrast, in a state death penalty case there could be a trial, a direct appeal to an intermediate state appellate court, then to a state supreme court, then to the U.S. Supreme Court, then to a collateral attack in the trial court, then a direct appeal of that to an intermediate state appellate court, then to a state supreme court, then to the U.S. Supreme Court, then to a federal habeas corpus petition in a U.S. District Court in the place of incarceration, then to the U.S. Court of Appeals (with possible en banc review), and then to the U.S. Supreme Court. This process would typically take 10-20 years. (Some states, like Texas, are a bit faster, some states, like California, are much slower, Tennessee would be in between.)
A direct appeal in death penalty cases in mandatory in some jurisdictions and can't be voluntarily waived, out of the desire to be assured that the conviction is truly solid.
Like, It makes me wonder that if the defendant asks for no appeals of
any kind, would that work to bring the date closer?
What you are talking about is called a "death penalty volunteer" and it isn't terribly uncommon in terrorism case for a criminal defendant to admit in open court in the most public forum available to committing the crime, unapologetically, in order to claim the case for the cause.
One of the better descriptions of what happens in the case of a death penalty volunteer can be found in this 2014 law review article which is reasonably up to date:
About 11% of those executed in the United States are death-sentenced
prisoners who sought their own execution.
These prisoners are commonly called “volunteers,” and they succeed in
hastening execution by waiving their right to appeal their conviction
and sentence. The same number of volunteers (143) have been executed
as death-sentenced prisoners have been exonerated (143). While the
exonerated have prompted scrutiny and condemnations of the legal
processes leading to their death sentences, the fact that volunteers
bypass legal procedures designed to ensure that only the “worst of the
worst” are executed has attracted considerably less attention and
effort at legal reform. This may stem from our uncertainty about how
to interpret volunteers.
Certain interpretations dominate. Those who oppose a condemned
prisoner’s request for execution often cite the prisoner’s history of
mental instability and frame the prisoner’s decision as a product of
suicidal depression. Related to this narrative is one that links death
row conditions to the prisoner’s decision to hasten death. Conditions,
in this account, contribute to the decision to abandon appeals by
wearing the prisoner down to the point that he loses the will to live,
or by contributing to “death row syndrome,” an evolving (and
controversial) psychiatric diagnosis describing a mental condition
that some prisoners develop as a result of living under a death
sentence in highly socially isolating and stark conditions of
Other narratives focus on ideas of rational choice and personal
autonomy. This account emphasizes prisoners’ desire to control their
own destiny and the civic virtue of respecting autonomy and choice,
even for the least among us.
Even in cases where someone convicted and sentenced to death tries to confess and waive appeals, imposing an execution would typically be at least a three to five year process, due to legal challenges over the fitness of the defendant to stand trial and the competence of the defendant to waive appeals, and over establishing protocols for carrying out the execution.