The master holds everything you have done. A branch is a role-specific copy with its own match score and its own wording; the Tailor saves one with the match before and after. Versions are snapshots taken before an import, before tailoring or before a restore, so the previous resume is always one click away.
A branch is editable: a copy of the resume aimed at one role, kept beside the master. A version is a snapshot you can restore but not edit, taken before something replaced the working resume.
Branches: two on Free beside the master, unlimited on Pro; older ones stay readable and exportable. Versions: the newest thirty, and the snapshots taken before an import or before tailoring are never evicted.
No. It works signed out and keeps everything in this browser. Once sign-in is switched on, an account is used only for a Pro pass, for applying to roles posted here, and for syncing your profile across devices.