They did use glazed ceramic tiles on kitchen walls in 1910, in either black or white, so even if the tiles were a later addition, they wouldn't neccesarily be out of place, or should I say time? Counters as we know them didn't exist, strictly speaking. Kitchen furniture was pretty much free standing, a cabinet here, a table there. Cabinets and china closets could be built in. Work areas were usually wood, or maybe a marble area for rolling dough. Zinc was used, as was tin, also porcelain enamel. In other words, any contenporary, durable counter that is pleasing to the eye and looks like it would go nicely with your tile should be acceptable. You can check out the Victorian and 1920's kitchen albums. You'll see that they started introducing built in cabinets and counters in the 1920's, but the vast majority of kitchens still had that19th c look. Try just introducing some turn of the century elements into your kitchen design. You might get ideas if you look at the pictures. Here is a link that might be useful: photo albums

If you have trouble removing the high spots it will probably be easier to cut out that section and and put up fresh plaster or use drywall. I tore down drywall and replaced it when I was trying to replace wallpaper because it turned out to be cheaper and faster than trying to strip it off. Also that way you have a nice smooth surface to work with.

The term "BX" is sometime used a little loosely but I'm going to presume you have some kind of metal jacketed cable without a ground wire. For those kind of cables, the jacket is the equipment ground. With type AC cable there is also an aluminum bonding strap but that can't enter the box. You need to either replace the box with a metal box or replace the cable with something with a "real" ground (NM-B [Romex] or metal clad cable, type MC). I'm not sure an old work box is designed to support a fixture. Maybe someone could comment on that.

It's probably a safe assumption that there will be lead in the lower layers given the age of the house, I think---not even sure I'd bother to test it. (They do test for free here, though---I wouldn't be surprised if Portland does too.) Lead was in virtually all enamel/cabinet/trim paint before the late 60s. But you can still sand with the sponges---that's what they're designed for, in part. When they're wet, they'll contain the dust so that it's not all over the place; a mask will also help to make sure you're not breathing it, and then afterwards you wet mop to get up any bits of dust on the floor. We did the whole lead testing and education bit with our county last year, and it was super helpful. One of the more important things I learned was that while lead is icky stuff, it's largely a concern if it's eaten or inhaled in quantities, so you can do a lot to prevent that and to let older kids know to avoid chipping paint and wash hands after touching it. It's also less of a concern if it's a one-time project than if it's ongoing chipping, like with a window where someone's painted the sash so every time it opens or closes, fine dust comes down. Projects can be more easily secured so toddlers and pets are away from the work. The really important thing they drilled into us was that the surface of the paint needs to be intact---you don't need to remove lead paint, but you do need to have it covered with a good layer of new paint on top. It's worse to take some of it off and open up lower layers to chipping/flaking than just to leave them alone and paint over with good quality paint, unless you have the resources (time, energy and/or money!) to strip down to the bare wood. In your case, I'd only touch it enough to get it into paintable shape. The biggest problem we had was our dog---lead paint chips apparently smell/taste sweet, which is what attracts babies too. So we would constantly catch him snuffling in an area where work was going on, trying to find the chips. Finally just gave up on that and shut him out of the room all together till we were done!