Help with hard wired chime and Video Doorbell Pro

Sorry if this is long, but I have hit the point where I need help. We installed the doorbell and all was fine for about 5 hours. Then our doorbell started chiming with no one ringing the bell and no notification that someone was at the door. It would ring about every 2 minutes until I got tired of listening to the dogs bark every time it rang. I took the doorbell off the wall and taped the exposed wires so they wouldn't touch. Checked everything the next day, and the wires for the pro power kit were a little loose on the chime unit. Tightened them up and reinstalled the doorbell. Also bought a plug in Ring chime to use in the office since we can't hear the chime with the door closed. Again after just a few hours it started chiming again. Took the doorbell off again. The video doorbell was warm and the app told me that the unit was off-line. Since I didn't get any notifications, I am thinking I need to replace the chime unit (it is about 30 years old). Looking at some of the ones listed on the compatibility chart and am considering BROAN-NuTone LA126WH, Heath Zenith SL-2796-02, Nutone BK105 and, Newhouse Hardware CHM3D. Only problem is that they match the 16volt requirement but they are showing for 10 or 15VA. Would it be a problem? Also hoping that my problems didn't fry my brand new Ring doorbell but I won't know until I can get this sorted out. I really need some guidance because my husband is getting impatient.