Google search engine and Google Chrome are two totally different animals owned by the same holding company. As I said above Google Search Engine as well as any other search engine has given HTTPS a bump in ranking for quite sometime.
The “Not Secure” warning started with Google Chromes July release. You won’t see that warning on any other browsers like Safari yet. You still should implement SSL as Chrome is by far the most used browser and the other browser will probably start issuing a similar warning.
Every different search phrase from different locations will give different results. As a website builder you’re not the search engines customer or sponsor. Their goal is to provide the best SERP page, based on what phrase the searcher types from what location.
If a searcher types “coffee shops” from Los Angeles, they probably don’t want Coffee Shops in New York or London. That’s called an implicit local search. If that same searcher is traveling to London and types “coffee shops London” they’ll get local results for london. That’s called an explicit local search phrase.
Years ago to get local search results you had to explicitly give a location, but now the search engines try to determine your location. You can get more information on how they find out where you are here: