Rename functions and variables.

Symbol naming was way too lazy. I renamed user facing variables and
functions in a better way and added the `apu--` prefix for all /private/
ones.
Move registration of last update day to `auto-package-update-now`.

When calling `auto-package-update-now` the last update day would not be
saved.

The last update day would only be saved when calling
`auto-package-update-maybe`. This commit fixes this issue by saving the
last update day whenever the actual update in fact occurs.