The new stock didn't go in using the lift (I don't think it would fit anyway - the cars are longer than the 1940 stock) The changeover was in 1993 - the new terminal was well under construction by then. Here is a picture of one of the old trains being craned out.
Yes, it's somewhere roughly where the Eurostar bit is now.
From memory, I don't think you could see it from anywhere that was public access within the station, but you could see it if you were on the inner side of Elizabeth House (the office blocks that front on to York Road and the cab road) - I'm probably breaking the official secrets act by saying so, but I briefly worked there in about 1988 as a very junior civil servant (it was the Dept of Education then) and would frequently find an excuse to go and visit an office on the inner side of the middle block to see what was in the yard (which was more interesting than watching trains between Waterloo East and Charing Cross which is the view I had) - although never saw the lift in action.
This picture on Flickr - www.flickr.com/photos/28083135@N06/5739308454/ - shows the lift - the photographer is facing more or less north easterly. The office building at the left of the picture is the 5 storey block of Elizabeth House that fronts on to York Road, the building at the back of the picture (that disappears off the top of the picture) is the block that is on the corner of York Road and the cab road.) These buildings are pretty obvious on the Satellite view on various mapping things on the web, so this should help pin the location down.
At the time I worked there, conjecture was that the building (or at least the older, 5 storey bit) would be demolished to make way for the Eurostar terminus
Sorry, for the sake of precision (!), we buried the lift when WIT was built; as norbitonflyer says, the stock changed over via the well in front of the depot. (Certain elements in NSE management tried to wind up the Department by suggesting that the new stock would go in via the lift and then have to be left there once the lift was buried - perhaps a ploy to get some extra funding at the depot?)
Yes, there was a stub off the northbound track - probably no more than 100-150m long as the lift emerged about 2/3 of the distance between the mainline buffer stops and the throat. The entrance to the stub used to be just about visible from the train but has almost certainly been sealed by now.