search problem

That’s standard behavior for the jQuery Autocomplete plugin. It only offers suggestions to the user as they’re typing in a field. If the user doesn’t select a value from the Autocomplete drop down the field behaves like a normal text input field.

You would have to disable the search form’s action. Either that or create a custom form within your theme and simply doesn’t submit to anything then target that input field within the Autocomplete plugin’s settings.

One way to disable the form submission using jQuery would be something like this:

$( "form" ).submit(function( event ) {
  event.preventDefault();
});