You can find these files in '../{segmentedFolder}/FCS/compensated' path. The name of the analysis will be the prefix in the FCS file name.
State JSON file
Your analysis state JSON file will be located in the experiment root folder.
Open analysis
If you want to open some analysis state then you should click on the 'Open analysis' item in the 'File' menu and pick analysis state JSON file that you want to restore.