The answer to all these questions (which I know have been troubling you for many years) is: sort of.
I’m sure you spotted this years ago, but I have only just discovered the ‘Traffic’ box on the right-hand side of Google Maps, where you can tick the Public Transport option, and – hey presto – see exactly where the tube lines run in relation to street-level reality. I’ve seen these ‘real geography’ (there must be a technical term for this) maps before, and I know that the very first tube maps – like the present Paris Metro maps – were more or less real, without the present simplification, and so with the kinks and the corners and the vast expanses between suburban stations left in. But I haven’t played around and explored the detail in this way.
What it doesn’t show is the zillions of miles you have to unknowingly walk when changing between lines that are theoretically at the same station – e.g. Green Park, Kings Cross, etc. At least Paddington, Bank, etc, have the honesty to have multiple white ‘station dots’ (more technical vocabulary needed please) linked with the white lines to announce that they are not really the same tube station but no-one has had the nerve to admit it yet.
There must be some site or app that brings to light these dark secrets of the Underground system. Do post one in the comments if you can find it.