Ring 3 (battery) + Ring Wired - and do I need the jumper?

I have a Ring 3 (battery powered, but also now connected to the doorbell wires) and a more recent Ring Wired. I’m assuming it’s ok to run both on the same doorbell transformer, right?

Second question - I’ve noticed that the Ring 3 battery shows wired on the app, but doesn’t every really charge. And I eventually have to pull the battery out and hook to a charger. That being said… I never used the jumper on the old doorbell. Is that why the Ring 3 isn’t changing?

Third question - I have an old chime. Wires are labeled 0, 1, 2, 3. Not sure what to jumper! (Pic added in comments).

Hi @user56382. When you hardwired a battery-operated Doorbell, it will receive a trickle charge. You can learn more about this here. Thank you for providing the picture. Unfortunately, I’m unable to tell you where you’ll place the Jumper Cable. I would look at the wires going to your Doorbell Wired and match them with wires on the back of it. Then just match the colors with the ones in your chime kit. Nonetheless, you can run both of the Doorbells on your transformer, as long as the transformer has an adequate voltage rating.