Drop Down Show Search Input Field

That is normal when you activate the enhanced user interface for the drop down, I am not sure if the chosen plugin gravity forms are using for the enhanced user interface provides a way of disabling the search field. That said you may try using css to hide it if you really don't want it by adding something like this to your themes style.css

.chzn-search { display: none; }

Edit:
According to the following topic over on the chosen scripts issue tracker it looks like they added the ability to disable the search field a few months back by passing the parameter "disable_search: true", but I don't think the chosen scripts included with gravity forms have been updated in a while so until they are updated in a future version of gravity forms I think your only option is to use the css above.

https://github.com/harvesthq/chosen/issues/772

Just to update this topic you can also use the filter gform_chosen_options to disable the enhanced user interface search feature when less than a set number of options are present or altogether.

You would add the following to your functions.php file

add_action('gform_pre_render','set_chosen_options');
function set_chosen_options($form){
?>
<script>
	gform.addFilter('gform_chosen_options','set_chosen_options_js');
	function set_chosen_options_js(options,element){
		// disable search if select has less than 5 options
		options.disable_search_threshold = 5 ;
		// to disable search altogether use options.disable_search = true;
	        return options;
	}
</script>
<?php
	return $form;
}

Find out more about gform_chosen_options and an example of how to limit the number of items which may be selected in a multi-select field on the following page of the documentation
http://www.gravityhelp.com/documentation/page/Gform_chosen_options

Regards,
Richard
--
Just another member of the community helping out where I can