The easiest way is to use Export function (Import/Export at the bottom of Tixati Settings) to backup settings and Transfers list in a .tixaticonfig file. In order to manually add partially completed torrents you need torrent data and .torrent file. You can easily save .torrent files for all transfers by selecting them and using right-click menu: Meta-Info > Save .torrent.
From what I tried on Windows:
Tixati has Import/Export function (in Settings). It works OK but has one downside: doesn't save boundary pieces for partial downloads. You can copy whole Tixati settings folder, install fresh Tixati and paste old settings (including boundary pieces). Tixati data files are located in %appdata%\Tixati folder.
