Reinstall the latest version of the jailbreak before updating. You must have JB >= 1.13.N in order to remain functional on firmware >= 5.6.x
The BackDoorLock may or may not have updates for firmware revisions released since you originally installed it, best check the dedicated thread.
No issues with calibre, although not every firmware "improvement" has met with approval. e.g. Cloud Collections annoyed lots of people.
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Issues with Amazon's Storefront... sounds like that might be fallout from (not applying) the March 22 critical update.