Questions: I don't even know if there is something that can be done about it, but the following sites make the toolbar disappear: spezify, baidu, answers.yahoo.com and a few more sites.
The simplest answer to this is that nothing can be done. The frame removing scripts on these sites removes the toolbar. In the near future I plan to make fefoo as a browser extension. Till then I don't think anything can be done about it.
Question: Maybe the script simply tries to get the favicon from the site, but the following sites don't show the favicon in the toolbar: docjax, gazhoo, about and a few other sites.
There can be a number of reasons for it. The favicon location has changed. Favicons are encoded in a format that the browser does not display. On one browser it might work and on another browser the icon might now work.
Feature request: Propose popular searches as I type in the search box
Its already there in the code but just not polished enough to be turned on for everyone. If you use fefoo from the browser toolbar you should get a list of popular terms as you type.
If you have a bug reports/feature request/ideas don't forget to send it across. You can email the ideas and requests to email@example.com or join the Google Group http://groups.google.com/group/fefoo if you have any questions or want some help. You can also send it out using the feedback form.