Would a 2nd global referendum be needed to ratify a Constitution of Earth, and would further global referendums be possible?
Yes, a second world referendum will be needed to ratify a world constitution, and a secret ballot would be needed (or at least preferred) for this process. As well, there will surely be a provision in the Constitution of Earth for other citizen-initiated referendums, although the costs in terms of money and time required to mount such a global voting exercise likely means that for the foreseeable future, only the absolutely most critical issues would warrant such action. (Technological developments may well dramatically reduce the cost of a global referendum in the future.