Does a SQL server unique constraint partially or fully fail a multi-row write? If some rows of a writing query fails a unique constraint, will only those writes be rejected, or will the entire query fail?
Every individual transaction (statement) in SQL Server is atomic, meaning it passes or fails as a unit.

If the 999,999th record fails on a constraint violation in a 1,000,000 row insert, all of the other rows get rolled back and the table is exactly as it was before the failed statement was attempted.

The same applies for updates and deletes, as well as multiple statements in an explicit transaction.  For instance, if I have an explicit transaction that does a DELETE followed by an INSERT and an UPDATE, if I encounter an issue in the UPDATE and issue a manual ROLLBACK all of those actions get undone.