How would they do that? Pass a law? Does the federal government have that authority?

They can do it without passing a law actually (which is a bit scary if you think about it.) Congress and congress alone has the power to determine its membership. They can simply pass a resolution stating that no member who was elected by a district that was gerrymandered by some specific criteria will be seated in the future. The courts can go pound sand if they don't like it.

Some of this has been litigated and it's not quite that black and white. Take a look at

https://en.wikipedia.org/wiki/Powell_v._McCormack

Yes, the court can make such claims as they do in Powell, and Congress can ignore them. It is pure power politics, but the reputation of the court has been so diminished that Congress could easily get away with refusing to seat a member or two and there is really nothing that anyone could do to stop them.

You can make that argument about anything, though and it be would be equally applicable. 'The branches of the US government can start ignoring each other'. Sure, they could but that possibility doesn't really offer any useful insight. It's like saying I can become world heavyweight boxing champion by shooting my opponents.

> How would they do that? Pass a law? Does the federal government have that authority?

Yes, at least for federal election districts. (The power is shared with the states, though.)

The crux of the SCOTUS decision is the court has no way to define fairness when it comes to drawing political boundaries. Congress passed a law banning gerrymandering using racial criteria, so courts can overrule maps on that basis. But Congress hasn't addressed partisan gerrymandering. The courts, rightfully in my opinion, after reading the SCOTUS opinion, are rejecting the right to unilaterally expand the set of criteria upon which they can reject political maps.

Probably not.

Wait, I am probably wrong about this; the Constitution explicitly delegates this power to the legislature.