Can I take photos with my mobile phone and record them with a Bluetooth headset or a voice recorder?

It seems possible, but if you really want to use a "mobile phone" to record images that can become memories in the future, then it is recommended to use something more professional to record them.

You can record it separately (but start it synchronously and trim it later. But it's best to record the memories after the wonderful moment without any pruning in the later stage. This is memory)