Will this address the gerrymandering in TN and other states?

I found it interesting that Doug Jones only had a majority in one AL district.

Does it deny citizens the equal protection of the law;

Arizona Senate votes to seize assets of those who plan, participate in protests that turn violent (link...)

does it deny them their First Amendment right of free speech and association by making their votes less valuable?

See link above. If you're in a 50-50% district, and the Party in control redraws it 49-51%, the new Party in charge could easily attempt to stifle speech and assembly.

And ultimately is that something a court can accurately measure?
If the court asks the GOP. They seem to understand it and find it very measurable.

It makes clear that using the redistricting process to inflict partisan injury -- to use the tools of government to subordinate one party and entrench another -- is unconstitutional. It does not preclude all consideration of politics or even partisanship. But it does say that a legislature can't use levers of state power to try to artificially (and) durably relegate one political party to second-class status.

Why the North Carolina redistricting ruling could end gerrymandering as we know it

This gets overturned, and (R)s control SCOTUS. Not to mention Anthony Kennedy retiring and that old gasbag Ginsburg can barely get out of bed in the AM.

This is, of course, another reminder to Republican voters that the Trump Train is having remarkable success in the courts. For whatever reason that doesn't excite the array of 3rd worlders and college dopes you guys cobble together to win elections. But Republican voters are woke when it comes to stocking the judiciary.

One of the fascinating things about how political parties use GIST to produce these gerrymanders is that the solution to creating "fair" maps is based in simple algorithms and GIST; however, the historical implication here is that fairness in maps becomes a matter of technocracy rather than judicial decisions. With a Chief Justice who talks about "sociological gobbbleygook," it is frightening that scientific ways of producing fairness might be set aside because SCOTUS members are not educated in how social science works and how technology is engendering social science solutions to human problems.

That said, I hope that we can see an end to gerrymandering out of this set of decisions. Like my father always said, "We can put a man on the moon, but you can't hear the referee at a football game." Think about that.

*My father ran radiotelemetry relay stations for the USAF detached to NASA on Apollo missions from 1969 to 1973 based in Greece. From 1967 to 1968, he was a forward air controller in Vietnam. Let's just say that he preferred the latter assignment to screaming "DROP IT ALL ON OUR POSITION OF DEFENSE!"

The Supreme Court Thursday agreed to freeze, for now, a lower court opinion that struck down North Carolina congressional districts holding that it amounted to an unconstitutional partisan gerrymander.

Supreme Court blocks court order to redraw North Carolina congressional districts

...Pennsylvania’s congressional district map is a partisan gerrymander that “clearly, plainly and palpably” violates the state’s Constitution, the State Supreme Court said

Pennsylvania Congressional District Map Is Ruled Unconstitutional