Thanks for clarifying your requirements.
You wrote “I appreciate a shortcode sample which covers, a hardcoded category name/slug, a search field based on “Keyword(s) Search”, a connector field (understood your hints).” I have developed an example HTML form and [mla_gallery] shortcode that meets your requirements. The example does not require any PHP coding and can probably be adapted to other search requirements.
You wrote “I guess categories and tags (available via smart media categories) will be covered when I add ‘terms’ to mla_search_fields.” Yes, that’s correct. You can use the mla_search_fields parameter to specify the fields you want to search. The example below searches all of the available fields; you can remove the fields you do not want to include.
You wrote “Is it possible to add a hidden search criteria as a MUST to a ‘Keyword’s search’ …” Yes, it is. The Smart Categories example plugin copies the terms assigned to an item’s parent post/page and assigns them to the item itself. In the shortcode you simply add a Simple Taxonomy Parameter to add a taxonomy term filter to the results, e.g., category="abc" in the example below.
Your application includes two different “connector fields”. In the example below, the AND/OR connector is handled by two HTML radio buttons. You wrote “AS means searching the phrase entered“; this is handled by the sentence shortcode parameter. In the form this is implemented by a checkbox. If you check the box, the sentence parameter overrides the AND/OR connector.
Here are the example form and shortcode parts for your application:
<form id="mla-search-form" action="." method="post">
<label for="mla-search-box">Text:</label>
<input id="mla-search-box" name="search-string" type="text" size="40"value="" /><br />
<br />Connector:
<input id="mla_search_connector" name="search-connector" type="radio" value="AND" checked="checked"/>
<label for="mla_search_connector_AND">AND</label>
<input id="mla_search_connector" name="search-connector" type="radio" value="OR" />
<label for="mla_search_connector_OR">OR</label>
<input id="mla_search_sentence" name="search-sentence" type="checkbox" value="true" />
<label for="mla_search_sentence">Sentence</label><br />
<br /><input id="submit" name="submit" type="submit" value="Search" />
</form>
[mla_gallery]
category="abc"
s="{+template:({+request:search-string+}|a-bad-term)+}"
mla_search_fields="title,name,excerpt,content,alt-text,file,terms"
mla_terms_taxonomies="category"
mla_search_connector="{+template:({+request:search-connector+}|AND)+}"
sentence="{+template:({+request:search-sentence+}|false)+}"
mla_nolink_text="Enter a search value above to display gallery."
[/mla_gallery]
I hope that gets you started on a solution for your application. I am marking this topic resolved, but please update it if you have any problems or further questions regarding the above suggestions. Thanks for your continued interest in the plugin.