Hi!
Thank you very much for your kind words!
1. I recommend trying the index table engine. That usually makes a great difference. The custom ajax handler is also a great idea – it will not conflict with anything. The disclaimer is mainly there, for WPML users, if the languages of the results are incorrect, they should turn it off.
2. That is indeed not part of the plugin. I assume the theme is automatically triggering it when the input value changes. You might have to ask the theme author if there is an option to disable that. If not, then maybe he can suggest a programmatical solution.
3. That is part of the theme as well, the plugin cannot affect the layout of that page. I assume you might be able to change them somewhere on the theme options.