Data is easily available at the county level in most states, the New England town level in some New England states, the Parish level in Louisiana, the Ward level in D.C., and the State House district in Alaska. Media outlets and state election administrators (usually but not always a state's Secretary of State) have this information available online and some county level election administrators also have online and precinct level data.
Most states have publicly available data down to the precinct level, but that information is frequently not available online (especially in more rural areas) and often has to be gathered laboriously on a county by county basis in abut 3500 election administration divisions.
Everyone in a precinct usually has exactly the same ballot questions and candidates, but sometimes multiple precincts have exactly the same ballot questions and candidates. A precinct typically has hundreds to several thousand residents, and almost never more than 10,000 to 20,000 residents. In NYC that might be a single block. In most places, it would be portion of a neighborhood or a full smaller neighborhood. Some precincts have only dozens of residents. My precinct in an urban residential area in Denver, Colorado is about a dozen blocks and would be fairly typical. In most reasonably densely populated states, the precinct is the base level of major political party organization with a precinct committee person or officer in every precinct where the party has members.
Voter turnout of 60%-70% of census population would typically be an upper limit of votes cast, and the typical percentage would be significantly lower.
In states that have partisan voter registration and voter participation information, it is available at a more fine grained level (to the level of the individual voter registration address) but usually only on a paid subscription basis.
The smallest unit used to draw legislative district boundaries is a "census block" since this is the smallest unit of census reporting and redistricting must be based upon census populations. The number of blocks in the United States, including Puerto Rico, for the 2010 Census was 11,155,486 (an average of about 300 people each). Census data at the block level is easily obtained as a public record if not online in downloadable files, a least in a public library reference that is a few years out of date.
"Party affiliation" is an ill defined concept with multiple operational definitions. One is to look at voter registration data in states that have partisan voter registration. Another is to look at election outcomes in fairly competitive contested partisan statewide elections to provide comparability between different parts of a state. It is also possible to sort campaign contribution data by partisan affiliation of a donee and zip code.