When I do google search, sometimes I ran into some websites that are also search engines. Somehow they know my searching term and do the search for me in their website too.
I want to ask how to achieve a similar result, letting others find my own meta search engine in google search, with your plugin. Is this something to do with SEO, or what? Can I auto generate a similar search page when people search on google, so they would find my website?
This plugin just display Google Search box and Search results on your WP site, but does not perform search task. The search is always done by Google, this plugin has not any effect on search results.
The plugin has not got SEO functionality, because there are a lot of very good WordPress plugins for SEO, and Google Custom Search will take into account SEO settings made by these plugins.
For further information you can ask Google, about how Google Custom Search Engine works.