These are excellent questions. When you click on Data Loader and you specify what Item Type you want (i.e. Tasks) you can then click on Advanced and select Field List, either as columns or rows. This will download a spreadsheet that will show you a list of available fields for that item type that you can upload.
I do not see Predecessor and Successor as available fields on Work Items or Tasks for that matter but there is a specific Item type called Dependency (Dependency Link) that should enable you to do this. This does mean that it will take more than one load. The first will be to upload your work items (Projects, Milestones, Tasks). Once you have this configured, you can upload the dependencies.
Note - Dependency Type refers to the Constraint type (Finish to Start or STart to start) and there is a field for Lag as well. see attached entity field spreadsheet.
Also, all Data Loader documentation is in the User Manual - http://usermanual.clarizen.com/data-loader
Did I answer all of your questions or do you have any further questions?