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.

What do you mean, the exe can't launch?  What happens?  Do you see an error message?  Please provide more details.

I cannot reproduce the issue.
Perhaps Chrome (you meant the browser, right? You wrote "chrom", which looks like a typo) is running as administrator?
Please see the following report:
http://tweaker.userecho.com/topic/308231-cycle-between-taskbar-buttons-stops-half-way-in-windows-8x/

So if my understanding is correct, the issue is that the tooltip is being shown for some taskbar items, but not for others. It's that right?

By default, the taskbar doesn't show tooltips when all the text is visible on the button, only when it's truncated.

Thank you for the detailed report, I could reproduce it.
Please try the latest beta version, which should fix this issue:
http://rammichael.com/7-taskbar-tweaker#download

The beta version adds support for Windows 8.1 Update 1 as well.

I don't speak German, but Google Translate gave me a rough idea about the bug.
What Windows version are you using? Does it work correctly when the tweaker is not running?