Voter registration databases are available from the Secretary of States office in each state. Anyone can request a file dump; however, some states often charge a small fee for the file. GOP and NDP use different tech stacks, but both are tied to companies (like NGP) that have built processes around obtaining and updating voter registration data yearly from each state. They then tie in historic data they have from door to door canvassing, voter turn out, and any other touch points to build a profile about the voter. Typical data points include voting history, gender, various voter level flags indicating if the voter supports causes/activism, and any other notes or voter related data.
Per-user voting history in many (most?) states. The fact that a ballot was received from a particular voter (but not what they voted for) is often releasable under public disclosure laws.
Yes, most states track voting participation at the voter level. Some track method of voting, other just are a boolean participation flag for each election.
Individual voting records aren't public in the US (secret ballot). However, whether or not an individual voted in a specific election is often public. (It may vary by state or other jurisdiction.)