1) Ajax results time depends on server response time and DataBase structure. Our theme does not have options to improve the results time because it’s related to how fast your server (DB) sends the response to requests made by theme. Try to improve the DB structure and speed up the server response time to get better results.
2) Search does not remove any symbols from the search request, how does it know when you want to remove “s” and when you don’t?
3) What do you mean by partial SKU? Could you provide examples from your site to check it?
