HELP! I have some issues...

While adding a pantry/closet I decided to rewire my kitchen light/switch, as the BX was too short to where I wanted to put a new switch. I pulled the kitchen light fixture and the drywall was charred, wires burnt, insulation cracking, etc.

I decided to trace out the wiring and replace the entire branch feeding the light (and two outlets). I put a toner on the hot to trace out the circuit, but then found it had some stray voltage on it. Put a meter on it and it read about 20VAC to ground/neutral with the breaker off. So I pulled the dead front on the load center and found that there is a 14/3 wire feeding both the kitchen light / garage circuit and another breaker - both are on the same phase. I killed the other breaker which removed the stray voltage, but I honestly can't find what the second breaker even powers.

Not being an electrician, my question is couldn't the two circuits on the same phase with a common neutral cause the neutral to be overloaded? Most of my wiring is older - late 60's but should be fine in my opinion (BX w/bonding strip). The insulation on the wires to the kitchen light fixture were brittle and cracking, and the drywall around the box was singed. All I can assume is that the circuits sharing a neutral should be on different legs, but I'm not positive on that. I pulled the hots out of the panel and tried to trace them, but they're all over the place - Can anybody with experience tell me why this might have been done in the past?

It's like Pandora's Box opening up this stuff. So many issues - In the attic, any newer circuit the previous owner ran with NM is just pushed into a junction box with the knockout half bent in - no connectors. And wire nuts? Forget 'em! Just twist and tape them together. Almost every switch I pull has blackened wires from arcing because they were so incredibly loose.

It looks like only two 15A breakers serve the majority of the house, with all the splices they did. My load center is an old Wadsworth, and I have no room to split circuits at this time.

Any insight? It's too hot in that attic right now!