Census is "actual Enumeration” of “all persons", so you'd need to join/filter the data to remove people who are not citizens. Doing so would cause some folks to be afraid/unwilling to fill out the census.
2020 census is especially difficult because they haven't done as much (any?) door-to-door canvassing that usually happens during a census.
Unlikely, as the census can’t share granular census information with other parts of the government for decades. You need improvements in how voting rolls are updated and kept current (I’ve seen voting registration been done at the same time as acquiring a drivers license or state ID at a DMV, for example).
There is a lot of power in leaning on existing online resources for performing this work, where your identity and address verification has already been performed (or it can rapidly be performed in a way that is both inexpensive to government and so frictionless it does not disenfranchise the disadvantaged). You just need competent government leadership and technology practitioners who can rapidly glue it together (I know, crazy high hill to climb).