Just to be sure, you are using the app from apps.ankiweb.net correct?
If you’re syncing with your account, it should download all the decks from AnkiWeb. Maybe give us some screenshots to see what is happening when you try to sync?
A change in Google Play Store polices forced AnkiDroid to start using a different file location on your device. That message is giving your options for how to migrate your storage from the old location to the new location. Read the options carefully and pick the one that applies to you.