I don't know the answer to the questions you asked in the first post. I'm under the impression that the search that's built in to vbulletin has limitations and a lot of people have been unhappy with it, but that's about all I know.
To answer your question about 'fop', one of the limitations is that there's a minimum word length which is set to 4 by default (in the adminCP options). The search uses a MySQL feature (full text search) which also has a minimum word length, so you'd have to change it in your MySQL server as well. I'm not sure if that would be a good idea, I think it's probably set to 4 for a good reason. I think if you set it lower it makes the index much larger and therefore makes searching slower.
There's also a list of "stop words" that are common words that can't be searched for (the idea being that they're so common that it's useless to search for them anyway). The default list is here:
http://dev.mysql.com/doc/refman/5.0/...stopwords.html (you can also read that section to understand more about how the search works).
Also, by coincidence I came across this thread earlier today, which might be of interest:
https://www.vbulletin.com/forum/show...search+plugins
Hope this helps.