The structure of tables and so are not inside the searchindex table. The search is not case sensitive, so there are no capital letters...
hitcounter and searchindex are the only tables, which use the storage engine MyISAM or HEAP. All others are set up to use InnoDB. Did they uninstall InnoDB or what?
If you want to proceed that way, you should do a row of search and replace operations for each page, e.g. "u800" => space, u82e => dot and so on.
When you start with the wiki all over again, do the installation and before you insert any content into the DB check the following:
- The character set for the DB and for the tables should be utf8_...something (e.g. "utf8_general_ci" or "utf8_unicode_ci"). If it is different from that remove everything from the new DB again and fix the charset first.
- Check that the tables are using InnoDB as storage engine. (hitcounter and searchindex should use something else, that's fine).
Btw: Have you considered moving to another provider? Seems like a good time to think about that.