Can I use Fast Backup on all profile types?

No. The Fast Backup option is only possible when no changes (other than being used as a backup* by SyncBackSE/Pro) are being made to the destination. This means it cannot be used with restore or synchronization profile types, or profiles that use prompting. It is for backup profiles only, i.e. files copied from source to destination, with nothing being copied back to, or deleted from, the source.

It is possible to combine Versioning on the Destination with Fast Backup, but you should see the caveats both here:

and in the contextual Help on the Versioning and Fast Backup settings pages.

* when using Fast Backup, any one Destination location should normally only be modified by that single Fast Backup profile. No other person or process (including any other profile of any kind in either the same or any other SyncBack installation) should normally be permitted to modify data in that location. Independent data changes can be dangerous if a Fast Backup profile is relying on the data in that location being unchanged.