> I am not sure but would say that the first two options are related to the py-launcher not the the python interpreter itself.

You correctly read the options, so we'll need a suggestion on how to make it more clear without becoming impenetrable. Maybe changing the third one to say "Install Python for all users" would suffice?

Possibly we should link to the install docs from the front page for people who want more help.

> OK, but why two options?

The py.exe launcher is totally separate from the version of Python you're installing, and if you previously installed it for all users (including if you previously installed Python 3.4 or earlier), you have to install it for all users again or it won't work.

The option is on the front page so that non-admins can easily disable it and still install everything.

> This appears on the first page ("Add Python 3.9 to PATH") and on the third page ("Add Python to environment variables").

So that users can change it without having to go through the advanced install. This is the most common option to enable, even though we recommend against it unless you know what you're doing, so putting it on the front page saves _many_ users from having to go through all the other pages.

> all this options are not synchronized

That sound like a bug. And I can't reproduce it, so we might need more info.

If you go through setup a few times (without ever actually installing) and fiddle with the options, it will still produce a log file in %TEMP% that should explain which settings were modified, so we can see why they may not be updating in the UI for you.