A good summary of the issues, AimHere.
I experienced the vanishing button thing once, but couldn't see any pattern to it. I had to remove the button, restart the program and re-add the button to get it back. The button, BTW, was that for Automatic screenshots—maybe that's more than coincidence.
Maybe some sort of dynamic resizing of the search bar components (so they all fit in the space available) would be the "least fussy" solution. It wouldn't give a perfect result in all cases, but would probably be better than requiring the user to adjust the widths (if that is even feasible). Otherwise, as you suggest, just making the text boxes narrower would go a long way to resolving the problem.
The search box is actually a combobox showing the dropdown arrow only if it is needed and the web search box is just a simple text edit box.
Good! Then the issue will be resolved automatically when you replace the simple edit box with a combobox.
I've always wanted some means for web searching terms other than the default
Original title or
Name. A combobox would be a perfect way to make other search terms available. What I miss the most is being able to use
Title instead of
Original title, but it could also be used for searches not involving the title, like
Genre and
Category for jumping to web lists of similar movies,
Studio and
Director for viewing sources like Wikipedia, and (I love this one)
File path for opening the video in
any program (e.g., an alternate player, analyzer, subtitle searcher, screenshot maker, encoder, etc.).