I think you are using an outdated version of the plugin. I believe the term title bug was fixed back in version 3.1. You can download version 3.2 from codecanyon. Please carefully follow the steps from the documentation when upgrading.
As for the taxonomies, there is indeed a limitation for 50 terms per taxonomy. (someone had like hundreds of thousands of them and the browser could not handle it)
You can disable it by disabling lines 109-110 in the ajax-search-pro/backend/settings/class/customtaxonomyterm.class.php.
if (is_array($terms[$taxonomy])) $terms[$taxonomy] = array_slice($terms[$taxonomy], 0, 50, true);Best,
If you like my products, don't forget to rate them on codecanyon :)