All I know is that it's caused by the updater mechanism. Unfortunately, the crash report doesn't provide many details, as the code is asynchronous. If you can come up with a way to reproduce the issue, please let me know, I'd really like to fix it.

Ticking the checkbox and/or creating an autostart manually will result in having 7tt as a background process.

That should be enough for the tweaker's options to apply. It's hard to say what the cause for your issue is.
How do you determine that 7TT is running in the background? Are you seeing the tray icon? In general, running the tweaker again should merely show the window, nothing more.

Implemented in the beta version. Please try it out.
http://rammichael.com/7-taskbar-tweaker#download

I don't speak German. Are you saying that 7+ Taskbar Tweaker doesn't run at startup for you, even though the checkbox in the settings window is checked?
Also, please specify your Windows version.

Fixed in v4.5.

Fixed in v4.5.

Fixed in v4.5.

Completed in v4.5.

Looks like that's an issue with your local configuration, not with the tweaker.
You have a restriction for applications that can be run.
Google for the error message you're getting for more details.