Can the New York State Judicial Branch refuse to issue a writ of mandamus when the executive branch defies the legislative branch?

QUESTIONS PRESENTED 1. Can the New York State Judicial Branch refuse to issue a writ of mandamus when the executive branch defies the legislative branch; 2. Can the New York State Judicial Branch give the Executive Branch fact finding powers; 3. Can the New York State Judicial Branch defy the legislative branch and assume power it does not have, by in effect rewriting a clearly written statute that is unambiguous, by way of its failure to issue a writ of mandamus; 4. Can the New York State Judicial Branch blur the lines that govern separation of powers; 5. Can the New York State Judicial Branch allow violations of the Establishment Clause.