A few questions/concerns centered around the transformer in pictures that I am pretty sure has failed. I'm not an electrician so I'll do my best to provide information but it's been a struggle for me so far just to understand what's actually there and etc., and I am a bit limited by what the person that built home left behind, e.g. unique wiring choices and "iffy" electric panel labeling. So please bear with me...note I am happy to break this into different posts/question if that makes sense.
The transformer is in my attic and attached directly to a junction box that has two live feeds (white romex-style wires) into it, and the switch right above it is the cutoff for my furnace located up in attic as well. A voltage tester pen-thing lights up when passed over all of the wires leading into the j-box, but when I test the output of the transformer with a Klein multi-meter for either (AC) voltage or current, I get nothing on the readout, or more correctly only when I touch the leads to the transformer contacts and then the meter registers something for just a moment but then goes to zero.
So I am pretty sure I need to replace the transformer...I wish I was 100% positive that it is the problem instead of just 90%, though. One thing that makes me confused and anxious is I am not exactly sure what this transformer is to...my doorbell stopped working several years ago but I now want to fix it (which is why I started investigating and DIYing). But I can't fathom why a doorbell transformer would be mounted directly to a j-box like this, and to the same box/circuit that the furnace cut-off is at/on? And it then begs the question...if this transformer (which I believe is bad) isn't the one for the house/HVAC system thermostat, which I believe also has lower voltage requirement and is clearly working, i.e. getting voltage/current from somewhere, then where is that transformer located?
So it seems the only way for me to know for sure if this transformer is bad, and that it is the one for the doorbell, is to replace it with a known good transformer and see if doorbell then works. So an additional question is making sure I understand how to remove and replace it...it looks like there is a screw on the inside of the j-box that tightens a hold-down thingy for transformer (hard to see from pic...poor lighting up there). I guess I can deal that pretty simply once I figure out how to make sure all current is off for the wires leading into j-box. But I noticed that the replacement transformers I see (Amazon, Lowes Depot) don't look like they have similar mounting configuration...should I care?
Chime Box Pics: