both hot and neutral lines have electricity

Question

I live in an old house built in 1960s in the US. A year ago, I hired electrician to upgrade main panel but did not re-wire existing 2-prong outlets. A few weeks ago, multiple of these 2-prong outlets stopped working while rest in the same breaker continue to work. The breaker never tripped. I had 2 electricians come out and I am not sure which one to hire or if their diagnosis is correct.

Electrician A tried to find the first outlet that works and is connected right before the broken one but couldn't find it easily. He said there is small amount of voltage running in the broken outlets. He said because my outlet boxes are very old and using crimp connectors and overtime it can cause loss connection, he believes there is 80% chance replacing all non-working outlet boxes and using wire nut could fix the issue. If this doesn't fix the issue, he would try re-wiring the next.

Electrician B said he would have to trace the line and do troubleshoot but he didn't say anything about possible loss connection. He said both hot and neutral lines are carrying electricity when nothing is plugged in and unplugged a small device I had plugged in because it is not safe to keep it plugged in.

My question is,

1. What could cause both hot and neutral to have electricity when nothing is plugged in? Quick search here shows wires could be touching each other? But wouldn't that trip the breaker?
2. Would you hire A or B? Never worked with A and I may not have working outlets after replacing them if the issue is not in outlet but in wire somewhere. But his explanation kinda make sense because no electrical work was done on my house when this happened. I've hired B for other jobs before but found him to charge 2x the average price and his work has been ok-ish.

Answer 1

Get a third opinion and price?

Replacing all affected outlets won't help if the problem is in the previous box, so I'd guess it as closer to 50%.

There are devices for tracing wires through walls, basically by putting a signal into the wire and then scanning for it. Apparently A doesn't have one; dunno about B. I've been tempted to get one and donate it to my local library's borrowable-tools collection; they're useful in exactly this situation. (I used one to find where a contractor had cut through a wire after their own folks, including their electrician, had no clue how to proceed.)