Google Sheets- Conditionally formatting a column and checkboxes based on checkbox TRUE/FALSE status

I'm trying to make a spreadsheet with a series of checkboxes in A and names (some repeated) in B; the final desired functionality is that when a checkbox is set to TRUE, all the names that match the one next to it are formatted and the checkboxes that would trigger this behavior are set to TRUE as well.

Current progress by using =COUNTIFS(B3,"Jake",$A$3,TRUE)

Currently I know how to make it behave as the above picture, and I assume that replicating the formula with different names and their relative checkboxes would be enough to cover the entire file, but I have two questions:

Is there a more efficient way of setting up this behavior for every different name and checkbox without manually changing all of them in repeated formulas?

Is there a way to replicate the desired functionality of also setting the relative checkboxes to each name to TRUE? The following picture is a mockup of what should happen upon manually setting a name's checkbox to TRUE.