Here are some initial thoughts about what work is needed for this issue. Comments are welcome – there are several items I'm particularly unsure about. In the meantime, I'll get to work.
The topics that need work in order to help people back up databases properly include the following (there may be more).
The material here is focused on the tasks alone. The introductory topic, "Backing up and restoring databases" (cadminhubbkup98797.dita), should be enhanced with enough conceptual information to help head off the problems people might encounter. The two online backup topics should insert the instruction to run SYSCS_UTIL.SYSCS_CHECK_TABLE before backing up. Similarly, the "Checking database consistency" topic (cadminconsist01.dita) should mention that the function should be run before backups.
It seems odd that the backup procedure needed to make roll-forward recovery possible is not actually mentioned until the "Roll-forward recovery" topic (cadminrollforward.dita). In fact, the topic "Using the backup procedure to perform an online backup" (cadminhubbkup01.dita) mentions only one of the four backup system procedures. Seems as if it should describe all four and when each should be used. I'm not sure under what circumstances the NOWAIT versions should be used, actually – the Reference Manual topics don't say.
The "SYSCS_UTIL.SYSCS_CHECK_TABLE system function" topic should include a mention that it should be run before backups, and a reference to the Admin Guide should be added.
All the material on the SYSCS_UTIL.SYSCS_BACKUP_DATABASE procedures, the SYSCS_UTIL.SYSCS_FREEZE_DATABASE and SYSCS_UTIL.SYSCS_UNFREEZE_DATABASE procedures should cross-reference the Admin Guide.
The "restoreFrom=path attribute" topic (rrefrestorefrom.dita) already refers to the Admin Guide. However, it implies that it is not possible to overwrite a database when you do a restore (as in item 4 in your problem list), at least if you use this attribute. Do the problems result from operating system restores rather than those that use this attribute? This may also affect the other attribute topics: "createFrom=path attribute" (rrefcreatefrom.dita), "rollForwardRecoveryFrom=path attribute" (rrefrollforward.dita).
There's no obvious place to insert specific pointers about backing up databases, since the information in this guide is generally more basic than that.
The "Product documentation for Derby" topic already mentions backups among the Admin Guide tasks.
The "What next with Derby?" topic at the end of the tutorial could use some major rearrangement and rewriting, actually. The Wiki page it most prominently points to seems seriously out of date and should probably not be referenced, at least not prominently – instead the material at the end (paragraph and bullet list) should be moved up to replace it. Also, the first place pointed to should be the rest of the Derby documentation – maybe a pointer back to the "Product documentation for Derby" topic.
The "Quick start guide for experienced JDBC users" topic should also add a paragraph pointing to the product documentation topic.
There are existing pointers in "Preparing to upgrade" (tdevpreupgrade.dita), "Creating, dropping, and backing up databases" (cdevdvlp42173.dita), and "Using in-memory databases" (cdevdvlpinmemdb.dita).
The following topics could use a pointer to the Admin Guide where backups are mentioned: "Upgrading an old database to use SQL standard authorization" (cdevcsecuresqlauthupgrade.dita), "Encrypting an existing unencrypted database" (tdevcsecureunencrypteddb.dita), "Encrypting databases with a new external encryption key" (tdevcsecurenewextkey.dita), "Encrypting databases with a new boot password" (tdevcsecurenewbootpw.dita).