Can I use this device while the phone is...charging?...connected to headphones?

It is recommended that you do not use the KardiaMobile EKG to record EKG data while your mobile device is charging or syncing, or if you are using attached or paired headphones. Doing so does not cause any damage to the mobile device or the KardiaMobile EKG, however it may introduce enough noise into the recording to cause the recording to be automatically stopped because of "Electrical Interference"  or complete and receive an "Unreadable" result.