I have read the intro to the zend manual, and as far as I understand I have to install the framework on my server... And my webhosting provider says they don't support that, so it's not possible...
It must be installed in order for me to use it and implement a search function of my mysql records, right?
Thanks
The Zend Framework itself does not require any specific server side extensions or additional binaries other than PHP 5. You don't need your provider to install it, you should not have any problems just uploading the thing - or even just the Lucene related parts of it - and getting started. The ZF can be used in other PHP applications without it "taking over".
No, you can simply use the MySQL LIKE operator to perform a basic search (e.g. title contains "stackoverflow", etc...), or more preferably use the MyISAM storage engine that has fulltext search capabilities.
See the manual for more information about fulltext index and searches : http://dev.mysql.com/doc/refman/5.0/en/fulltext-search.html
But AFAIK, nothing prevents you from uploading the Zend Framework yourself, and use it as usual. The only thing is that you may not be able to write files out of your apache directory (which is required for a standard zend framework folder structure), so check this article on how to set ZF up on a shared hosting.
Yes but you dont need to install the entire framework, just the tedpendencies of Zend_Search_Lucene. But all you have to do to install is upload the files and make some include path adjustments, then require the nessecary files.