If a push fails partway through, do I lose tasks or get duplicates?

No. Pushing is resilient: it does each task independently, and if some fail the others still go through — the failed ones stay unpushed and are retried on the next push. The status line shows how many succeeded and how many failed, and the progress panel names which task failed and why (e.g. an app rejecting an over-long title). Todoist and Reminders also avoid creating duplicate copies if a request is retried.