Newer versions include an error code along with the "Could not load library" message. What error number are you getting?

That's already possible, please see the FAQ here.

Seems like a duplicate of this issue, with a slightly different scenario:
http://tweaker.userecho.com/topic/308231-cycle-between-taskbar-buttons-stops-half-way-in-windows-8x/

Looks like a duplicate of this:
http://tweaker.userecho.com/topic/164567-custom-date-format/

And indeed, there are tools which provide similar functionality.
In addition to the one you mentioned, there's also T-Clock, which you might want to try out.

As far as I remember, the hotkeys are global, i.e. it won't be possible to reuse the code for a single button group in a straight forward way.

I'm not sure, but I think that it has to do with the system visual theme.
Also, there's a topic about it already, so closing as a duplicate:
http://tweaker.userecho.com/topic/406829-/

What is your definition of "in focus"? You already can choose to skip minimized windows.

That's an intended behavior.
First, when a Metro app process is killed, the taskbar button doesn't go away. You can try it and see.
Second, I'm not sure how Metro app processes are implemented. Perhaps it's possible that two apps share the same process, I don't know.
Why would you want such functionality? As far as I know, Metro apps don't tend to hand like native apps sometimes do, so it's usually enough to just close them.

Yes, you can create a shortcut with a predefined AppID. A tool which can help you with this is win7appid.