The solver works locally in your browser, so the puzzle is not uploaded and no account is needed. It uses constraint checking plus backtracking: it tries the cell with the fewest legal candidates first, which avoids much of the blind searching done by a simple left-to-right solver.
Duplicate digits are highlighted before solving. A puzzle can also be valid so far but impossible to finish; in that case, the grid stays unchanged and the status explains that no complete solution exists.