Is there a connection between the character, Molly Solverson and any other character of the Fargo movie? I wonder if there is a connection between Marge Gunderson and Molly Solverson, like heritage or something.
No, Molly is not related to any character from the feature film but her dad, Lou Solverson, does connect with season 2's story that takes place earlier in the 1970s.
The only firm connection season 1 makes to the feature film, is how Stavros Milos (Oliver Platt's character) came up with the money to start his business, which was left behind by Carl Showalter (Steve Buscemi's character) from the events of the Fargo feature film.
"In a flashback, we learned that Stavros happened upon a suitcase full of money buried in the snow on the side of the road after his car broke down. He made the lucky find after glimpsing a red ice scraper stuck in the snow by a nondescript fence. Stavros took the money for himself and used it to start his company (which takes us up to the "present day" of the show: 2006)."