No fees to google. You do need to register with the developer console and use site index. Then pay for other services that analyze your site and competition and tells you what to fix and change etc. Backlinks are important. And what site score the sites that use your links have. Some with bad ratings you need to get rid off etc. Basically tell google to unlink you from the bad sites.
One thing i did was create and purchase old urls and create content there and link back to here and other sites. Whats known as “authorative” sites.