I want to create an app that promotes a query to google search by specific filters and restrictions i put in place and then show the results to the user (specific keywords in results for the past x days). How can this be done?
Can this be accomplished by using the Google site search https://www.google.com/work/search/products/gss.html together with this API: https://developers.google.com/custom-search/json-api/v1/introduction#background-data-model
Has anyone tried something similar?
Yes. it's possible with restrictions. You can use only GoogleCustomSearch (your links above)
Using Get template create an request (https://developers.google.com/custom-search/json-api/v1/using_rest)
GET https://www.googleapis.com/customsearch/v1?key= YOUR_KEY&cx=YOUR_CX&q=site:lenta.ru&siteSearch=lenta.ru