On what request to cache the search?

Question

caching

Hello!
How to suggest what the user wants based on his previous search queries, even if not on our site, but from cookies, take several queries in Yandex, for example, run in the background through our search, and if there is an issue, then show?
+ it is necessary to show what the user has looked at before, if the user has also looked at a separate task, probably, set up recommendations for products, that is, if a person has looked at at least one product, he was shown those recommended for this from other sections.
How to find out what request came from the search engine?
Is it possible to find out which sites the visitor has visited before?