free search issue and listing content issue

1) This explains how the search works: https://wpgeodirectory.com/docs/core-design/#how

2) Have a look here: https://wpgeodirectory.com/docs/core-place-settings/#custom

1) The link is not only about the location search:

GD will check the entry titles, description and taxonomies (tags and categories) of the listings.

Post the URL of the listing you are trying to find and we can have a look. It is possible that the issue is the hebrew so be specific about what you are trying to search for and what you expect to find.
Also, the problem might be that your site is in a subdirectory matching the word you are looking for.

2) Look at the link again and look for “Show on listing page”.

3) WPML is only required if you want a site in more than one language. If a user wants to submit a listing in a specific language, he has to choose that language first.
But your site does not seem to be multi-lingual, so then there is no need for WPML.
Your users can add a listing here: http://outofsite.biz/yoga/add-listing

I hope I understood your questions correctly. Thanks.

1) titles, description and taxonomies (tags and categories), not only tags and titles.
Cannot search anywhere else like custom fields.

2) Have another read, it is there: https://wpgeodirectory.com/docs/core-place-settings/#show-on-listing-page
Setting this to YES will add this field to the relevant Listing and Search page.
Go to your custom field you want to show or not and change that setting.

3) WPML just creates a different site if you have different languages. So a user will have to submit the listing in all languages if he wants to be listed in all languages.

2) Listing page is the page with the grid; I think you are mixing up detail and listing page. There is no grid on the detail page for each listing, only on the listing/category or search pages.
https://wpgeodirectory.com/docs/layout/#directory

To NOT show ALL details of a listing in the results, go to your custom field you want to hide and change the setting “Show on listing page” to NO. Have you tried it already? There is no need for CSS (but you can use CSS if you prefer).

Or do you want it different on search pages like
http://outofsite.biz/yoga/?geodir_search=1&stype=gd_place&s=+&snear=&sgeo_lat=&sgeo_lon=
than listings/category pages like
http://outofsite.biz/yoga/teachers/studio/

In that case it will have to be CSS.

In that case it will have to be CSS. I just was trying to make sure you were not confusing the detail page with the listing pages.