> -- First and simplest, there is an application using embedded and I want to password-protect my database so that if anyone gets hold of the file they will not be able to read MY data without knowing the password or investing time and qualified effort in breaking the encryption.
>

There is one more related issue - I want to distribute some database and
be sure that noone except my application will be able to read data from it.

> -- Also completely unrelated: I don't want anyone to be able to see my data while in transit on the network - either LAN or the internet. Part of this - I want to be sure that I'm connecting to my server and not to someone pretending to be.
>

This can be achieved using authentication plugins in another direction -
client asks server to confirm that this is really your server.