The suggestion of simplifying routes, so that most/all trains from Blackheath head for St John's then Cannon Street, and most trains from Hither Green/Ladywell head for Charing Cross/Victoria regularly comes up. I think it would be a great idea, as it would make services far more robust. The only problem with it is political - whenever this kind of thing goes out to public consultation, loads of people and politicians start jumping up and down and screaming that they can't possibly lose trains going to several different London terminals.
I don't think that would be a good idea. Lewisham is not only an important destination in its own right (huge shopping centre, bus interchange, and lots of housing nearby) but a significant interchange for rail and DLR journeys - and will become more so when the Bakerloo line arrives. If routes are rationalised, you'll have even more people changing there too. If anything, I think a very important requirement is reduce, not increase, the numbers of metro trains that skip Lewisham. Ladywell by the way is the station for Lewisham University Hospital - so I'd say Ladywell trains really need to stop at Lewisham in order to allow more general travel from SE London to the hospital.
It's pretty close to Lewisham, so you could probably get away with closing it if necessary. But I can't see how closing it would help Lewisham.
I'd say, not too bad if you're at the London end of trains, although the subway is a bit unpleasant and I'm told can get very overcrowded in rush hours (I only really use Lewisham off-peak). Pretty terrible if you're at the 'country' end of a train because then it's invariably a very long walk to get to the other platforms. A cursory look at Google Maps should show how far platforms 1/2 are from platforms 3/4 at the country end.
Dunno.
There's been some talk of it doing so. The Hayes line is the most obvious choice, and might possibly not be a bad idea, but would need to overcome some public opposition. I'm not sure if it would also mean an extended closure of the entire Hayes line for converting to LUL electrification. (But on the other hand, if Lewisham was going to be rebuilt, you're going to have a lot of extended disruption to a LOT Of metro lines anyway).