How do I change the title at search page?

“search place …” can be changed with the language file, by changing “Search”.
“Places” is there because that is the plural name of the custom post type [CPT].

For example, see https://classicalcitizens.com/?geodir_search=1&stype=gd_string_teacher&s=+&snear=&sgeo_lat=&sgeo_lon= and you will see “Places” is replaced with the plural name of the other CPT.

You cannot delete the Places default CPT, but you can rename the CPT. Or if you delete all places and place categories, the CPT will disappear from your public website.

The “titles and meta” is for the meta data only, not for the display on the page. For the search page, you need to use %%search_near%% instead of %in_location_single%

1. You can add the GD Search widget anywhere you like, see https://wpgeodirectory.com/docs/layout/#directory
To add it to the Events page, you would add the GD Search widget to the GD Listings sections at Appearance > Widgets.
See also https://wpgeodirectory.com/docs/widgets/

2. Not sure exactly what you mean. DO you want to remove “Events” from the CPT search options?
https://wpgeodirectory.com/docs/gd-search/#cpt
That can be done by adding this CSS:

.search_by_post option[value=gd_event] {display: none;}

To only hide that on the homepage:

.home-page .search_by_post option[value=gd_event] {display: none;}

Let us know if I misunderstood.

Look at the body classes for the events pages, you’ll see this is added “post-type-archive-gd_event”
So the CSS would be

.post-type-archive-gd_event .search_by_post option[value=gd_place] {display: none;}

etc. Adding “!” does not work there, so you will have to add the code for each CPT.