Today I got up and found myself able to edit other peoples questions and answers:
with the following quite low reputation and restricted privileges:
I'm happy you respect and trust me, but I'm trying to be as honest as possible; this is a bug.
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It's a part of the new development they're doing. Apparently it's being turned on for a day, disabled, reviewed, improved, repeat, rinse until profit is achieved.
This is not a bug. The team is currently conducting tests for a new feature that allows new and anonymous users to make edits to the posts pending these changes been reviewed by a high-rep user. They have been turning this feature on for several hours at a time. There have already been several sessions of these, as announced in the MSO Chatroom - see these conversation for instance: