Where is the share preview data cached? Does it have a retention period?

The location of the Share Preview data depends on the location of the Data folder.

For example, if the data path is E:\inSyncStorage, then the location of the Share Preview is:

E:\inSyncStorage\__preview__

Note: This is applicable for inSync On-Premises only.

Can administrator restore files and folder deleted by inSync users from inSync Share?

Administrator has no control over the files and folders deleted by inSync user from inSync Share. Therefore, administrator cannot restore such files. Only inSync Client users have a provision in inSync Web from where they can restore deleted files and folders. The procedure to restore deleted content through inSync Web are described under Restore deleted content section of inSync Client documentation.