Where should I see the "v1_retired" error ?

It looks like you're trying to use the old API v1 Sync SDK for Android. That does use API v1, so API calls made by it will fail now. I don't have an example available of exactly how they would fail though. (The Sync SDK had some offline and retrying functionality built in, so the failure may not be immediately obvious anyway.)

In any case, you should migrate to API v2. For using API v2 from Android, we recommend using the official Dropbox API v2 Java SDK:

https://github.com/dropbox/dropbox-sdk-java

There's an example Android app here:

https://github.com/dropbox/dropbox-sdk-java/tree/master/examples/android

Your AndroidManifest.xml should be set up as shown here:

https://github.com/dropbox/dropbox-sdk-java/blob/master/examples/android/src/main/AndroidManifest.xml#L33

You start the flow by calling startOAuth2Authentication as shown here:

https://github.com/dropbox/dropbox-sdk-java/blob/master/examples/android/src/main/java/com/dropbox/core/examples/android/UserActivity.java#L36

You complete the flow by calling getOAuth2Token as shown here:

https://github.com/dropbox/dropbox-sdk-java/blob/master/examples/android/src/main/java/com/dropbox/core/examples/android/DropboxActivity.java#L22

Your app can store and re-use the resulting access token for that user, as the example does here:

https://github.com/dropbox/dropbox-sdk-java/blob/master/examples/android/src/main/java/com/dropbox/core/examples/android/DropboxActivity.java#L24

Once you have an access token, you can make a client as shown here:

https://github.com/dropbox/dropbox-sdk-java/blob/395d463840778b4c6ec730aef82b0a9dbee10f8e/examples/android/src/main/java/com/dropbox/core/examples/android/DropboxClientFactory.java#L21

With a client, you can make whatever calls you want, as shown in the readme and examples:

https://github.com/dropbox/dropbox-sdk-java/blob/master/ReadMe.md#try-some-api-requests