I have no idea what UK law is. In the US the data itself is public domain, but the compilation is of data is copyright. Maps commonly would intentionally have errors in to detect copying - the error is creative work and so a copyright violation to copy so if someone copies your map you can sue them for copyright violation for not just the errors but also that compilation. If you take someone else's map and then use that to create own map off of (thus finding and fixing the errors) it is legal, but that is as much work as just creating a map from scratch.
Not by default, at least in the US. The database has to actually be more than just a compilation. It's not a high bar to clear, but it's there. Europe and the UK have the "sweat of the brow" doctrine however.
We have a database right in the UK, originally derived from EU legislation. That would apply to postcodes AFAICT, but government can legislate in favour of the demos and against a private corporation.
It can be, but that has unknown long term effects. If you do this it shows everyone your government cannot be trusted and so other good ideas will not happen because people cannot trust the government. We probably do not agree on what is a good idea so I'm going to leave this vague - whatever your political side there is a good idea that is suddenly unworkable because the government cannot be trusted to hold their end of the deal.
Yes, every other Royal Mail that benefited from a nationally compiled database would also be at risk of having the database they didn't pay to create opened up... meaning they could continue to use it in exactly the same way.
How devastating. /s
If you benefit by paying politicians so you can 'steal' national assets then why shouldn't we go after some of those assets. We're not even talking about depriving then if the asset, only making a copy of it.
Yes, it would be nice. There is at least now a presumption in favour of releasing everything under an open licence, but OS maps are one of the exceptions.