Photoshop Elements is a perpetual licence. That means you can use it for life or for as long as your computer operating system supports the software.
Upgrades are not free but upgrade pricing is available to owners of any previous version of PSE. But it’s best to shop around as on-line pricing e.g. Amazon, Costco etc. can often be less than Adobe’s upgrade price. Buy whichever is cheapest.
There are no free upgrades. Adobe sometimes issues a free update. For example PSE 2020 was released last October and there has been one free update in January 2020 plus raw file support for new camera models. As soon as a new version is released there are no further updates for previous versions.