It should fit straight on without modding Nige. It's an original seat. Have you made sure the tank is fully fitted on it's mounting rubbers? I always use a little silicon grease on them to help the tank slide home.
As for the questions, the studs are individually welded onto the base. The seat latch hole should be your focal point for where it should fit. You've got a small amount of movement on the hinge plate.
I found it easier to fit the seat pan to the frame before having the frame done and the pan as well. They don't fit very well TBH, when you see them bare you realise how much isn't really doing it's job, the back rubber for instance doesn't touch the frame, it needs another 3mm of rubber stuck on it, that's why the seat breaks in the middle, the weight of a passenger forces the back of the seat down and the rider forces the front down, somethings got to give and it's always the seat pan. The front rubbers don't always fit around the frame tubes either. Took me a fair while to get the seat to fit on mine and that also involved modding the seat lock a little, it would lock but not release. Fitting the seat before having the frame coated also shows what's been twisted over the years, the hinge pin brackets on the frame as a prime example, the back one always seems to be pushed down, maybe that's because of the distortion going on when you take a pillion on board.
If you're having the seat recovered then remove the seat cover and foam and fit the pan bare, get the pan coated, the rust from the top down, so it may look pristine from the bottom but it won't when you remove the foam. The recoverer will thank you for a rust free seat pan. Get the seat to lock and release easily, even if that means the seat hinge isn't fitted, then see what you need to do to the hinge to get it to align. Easy when it's bare metal, not so much when it's covered.
Check the threads in the captive nuts fitted to the pan for the seat hinge, cut off and replace if they look dodgy. I used flanged stainless nuts on mine. Check for cracks in the pan near the seat lock and hinge plate, down the side is where they go.