> - How can a spam caller call me with a source phone number that does not exist?
The same way they make a call with any source number. The two source numbers in a call (ANI and CallerID which don't need to be the same) have historically been not required and not validated. See stir/shaken for a modern effort to change this. Coming soon to a carrier near you; maybe.
Being able to set the source number enables many useful things as well as some spam/harassment/fraud uses. It requires a lot or coordination to allow the former and restrict the latter.
TLDR: don't trust caller id. Don't call people back unless you know the number/it's an expected call.
> - Shouldn't my mobile phone network verify that the caller - which was also inside their network - is a valid subscriber? Otherwise, how can they bill someone for this call?
Call billing records don't use caller id in the way you're thinking. If you pay for incoming calls, they're charged regardless of the source number, but it's recorded for informational purposes.
For outgoing calls, the call record is made closer to the source and is tied to the line that made the call, not the source number.
For intercarrier calls (which almost certainly the case here), the source carrier bills its customer and the interconnecting carriers count minutes on calls and settle up for net difference in flows (calling carrier pays, but interchange fees are going to zero among US carriers)
> - How does this kind of scam call work technically?
Get a phone account where you can set the caller id and calls are cheap; call a lot of people; successfully scam one or two; take the money and run.
Some voip accounts let you set caller id. Traditional primary rate interfaces (T1) usually do too.