Hello Jennifer, Sounds like a lovely idea! For wood stain, it may be that you can just sand the doors to remove the stain. If it was painted I would have suggested a heat gun, scraper tool and sanding or Nitromors scraper tool and then wire wool, water and sanding.... Hopefully the wood stain might be a lot easier to manage! Especially if you have animals or nippers around... For the locks... It could be straightforward If you can align the rim lock and door jam so it's in line with the holes in the door.. I'm no chippy here! So maybe you might want to hire one to do it for you, it's a small job really but one you want done right.. I have a collection of old doors someone didn't want with loads of holes all over the place from previous owners....(I made them into a screen).. but I could see all the botch jobs that had taken place over many years...... : )) The box lock as they are known is a surface mount whereas other styles aren't so you may have to do a bit of filling depending on what is already in situ.. There are lots of helpful tutorials on youtube one here you might want to have a look at too..So a few ideas.. : )) https://www.youtube.com/watch?v=hlCnfI64zgs

That looks like the original catch. My parents have the same on their understairs cupboard, works really well and it's a nice design. I would keep it, but perhaps remove old layers of paint and then repaint it.

I think the height is irrelevant because every door is different. So I think you have to buy a long spindle and place the knob or handle in the centre of where the cross bar would be (if it were a solid door rather than hollow) This picture of an old door shows the traditional placement

I like continuing a theme so if the handles match something else then that’s good- but not essential so don’t worry if something else doesn’t match. Separately I think on a door with strong geometric lines perhaps a handle with a square rose would be a better choice.