Are all current SE policies included in the Help Center?
Generally, yes. Behaviorally speaking, the Code of Conduct and the Expected Behavior entries in the Help Center are general guidelines when interacting on the site. Following the "How do I ask a good question?" and "How do I write a good answer?" entries will help with general knowledge on how to contribute your knowledge to your chosen site.
The example "policy" you mentioned has more to do with general accepted behavior than a written rule. Speaking of which, the "don't bump old posts" guidance could be more accurately written as "don't unjustifiably bump old posts." If you have a substantial edit or well-written answer, then there's no reason why you shouldn't be able to bump an older post with that action.
Are there some unwritten policies? If so, why are they not written in the Help Center?
Well... There aren't really any unwritten policies, per se. There are just some general guidelines frequent contributors and moderators would prefer users followed while contributing. Sometimes this is called "etiquette".
As an example, if you're frequently editing your own question to "bump" it to the top of the Active list, and you're doing so persistently, a moderator or higher-reputation user might kindly ask you to make more substantial edits before doing so again. This isn't because they don't care for your edits or your question, rather they would prefer you didn't bump your post very frequently. They also would hope that you got your question or answer's content right the first (or third, or seventeenth) time.
Normalized behavior like this isn't defined in the Help Center because, depending upon the norm, it varies by site. More often than not, it's talked about in that site's Meta site. Drones and Model Aircraft was recently created, and they've routinely had discussions about how to handle various behavior, how to guide newer users on editing correctly, and other topics.
To wrap it up, the Help Center's policies provide a global guideline for participating on the site. Per-site etiquette is something learned over time as you become more familiar with the sites in question. If you do something frowned upon, don't sweat it, simply correct it in the future. We don't hold grudges here.