Black stove pipe (and furnace pipe, for that matter) should be securely fastened together at each joint with no less than three sheet metal screws or pop-rivets. Stove and vent pipe should be inspected at least yearly, and replaced when signs of rusting or wear are evident.
When planing a major renovation project you will increase your chances for a successful outcome if you hire a contractor with whom you feel comfortable. Make sure the contractor has experience in renovation. Always check references and make every attempt to see current and/or previous work.