After opening DaVinci Resolve or DaVinci Resolve Studio go to Workspaces -> Scripts.
No, your original key you downloaded will work. If you haven't ever purchased AutoPod you can purchase it through the regular portal.
It works on all versions of Resolve Studio. For the Free version you must be on Resolve 19.0.3 or earlier. DaVinci had an update in Resolve 19.1 that stopped all scripts from working in the Free version of Resolve.
If you have any bugs or issues, please contact support@autopod.fm