Executives are neither necessarily single seat nor necessarily directly elected. When indirectly elected, the electoral body that is itself directly elected need not be elected with single-winner methods. The US, in fact, uses multiwinner elections for electing the electoral college now, though mostly using the specific method (multiseat plurality winner-take-all) whose manifest unfairness and utility in excluding minority voices is the specific reason for the existing statutory ban on multiwinner elections for Congress.
No, they wouldn't, as the problems (including duopoly) predate the changes you would reverse.
To the extent those are relevant, they magnify the problems now (with or without more districts), rather than mitigating them.
> It would be a lot harder for two parties to completely control an 8000 member congress or gerrymander that many districts.
More districts make gerrymandering easier, not harder. As does more information.
Sure, there'd be more independents (absolute count), and at least one more often, in an 8000 member House, but proportionate to the total, there'd probably be fewer, on average, than there have been with the 435 member House.
Single member districts are a disgusting thing for a society that claims to be a representative democracy. As a very simple example, rural liberals and urban conservatives effectively never get represented in our government, and that's still within the context of the false dichotomy of left/right.
But single winner ranked choice voting is still important for elected positions that necessarily must be one person, like executive seats.