No the download links are the public free version of the game. The early access is for supporters only. I can't post the link here because of itch rules but you can find the links in the devlog post. Yes you can use your old saves even on android.
Depends, are you on windows, mac or linux, just copy and paste the entire save map into the www folder.
If you played online the save files is located on your local db and should show up automatically. If they don't you either played incognito or recently deleted files saved on your local db.
If you play on your phone it should show up as well. Here I'm not really sure where the game saves the files but they should show up even if you deleted the old app before you install the new, best practice is just update the old app as it will ask you that.
