Based on a reasonable response for Stack Apps, this has now been done.
Merged stack-exchange into support (which many of the questions already had) and deleted support from those posts where it didn't apply.
These 24 questions were affected:
At the moment the number of tags allowed on a question is 5. Both client side and server side this limit is now1 enforced at the time of posting.
There is no direct limitation to allow 6 or even 7 tags. As a matter of fact, this query shows 1038 questions at the time of posting that have 6 tags. The revision for one occurrence reveals what caused that 6th ...
No, this information is not exposed via the API (and it's not available in SEDE either). The same question was posted here on Meta Stack Exchange.
User @rene found a way to scrape it from the website; see here for his solution. It could be that the rename / new functionality (tag favorites -> tag watching) broke it, I haven't tested it.
While this isn't possible with the API, it is possible with SEDE, if you allow for up to 7 days of lag.
Here is the SEDE Query that lists Tag wiki and excerpts in descending edit date order:
when w.lasteditdate > e.lasteditdate