I don't have any hard evidence, but I suspect that the people who have already jumped ship from GH only did so with solo projects or with very small teams. The switching cost for those people/teams is always going to be pretty low.
Looks like a good project. You should probably mention very, very early on in your docs, though, that this is for Bitbucket Server (self-hosted) and not for Bitbucket Cloud (bitbucket.org).
That depends - is that data encrypted on your system? Since git is decentralized, there's a chance that any plain-text copy (such as a clone on your system) could be compromised. Keybase even addresses this in the FAQ, to an extent:
> What if my computer is compromised?
> Your work is only as safe as your endpoints, so we can't help you there.
This applies regardless of host or protocol, BTW, and it isn't even specific to computing. (It doesn't matter how many locks you have on your front door if you leave the back door propped open.)