This depends on what device you're using. Unfortunately there are some devices that run broken/flawed versions of Android. What device are you using?
I'll need a bit more information on this. If you're exporting from the desktop app, you shouldn't be using the "Import" feature on Android. Once you copy things over, and use the right folder, all your games should just be there, favorites included.
Actually, it sounds like (based on your second paragraph), that you do have favorites working and they're listed first. We could add an option to show a favorites section, yes, just like Recently Played. You're the first to request it though. Consider it requested.