I much prefer to stone the deck, then drop the tub in so the tubs' rim covers the stone. If you butt the stone up to the side of the tub's rim, then you need to work harder for a cleaner line on the edge of the stone. Account for the thickness of the stone when you pour your mortar bed to set the tub in. If you're going that route. If uncertain, you can dry set the tub on top of the stone, peak underneath, see how much space you have between the tub's base and the subfloor. Then pull the tub, mix and set your mortar bed, then reset the tub and get the rim down nicely on the stone. Then drink beer while the mortar bed cures. Several beers. Mongo

once you install the cement board (so that it sits above the tub flange), fill in that channel with thinset, and let it harden. once hard, go ahead and install your Kerdi, so that it's sitting no more than 1/8" off the tub. Then you can seal it with Kerdi-fix. That's the "book" explanation. If it were me, I'd use the same color siliconized latex caulking as my grout and seal it with that. Reason being that then you wouldn't have to worry about the color of the Kerdi-fix sticking out from under the tile.

This long and narrow bathroom reminds me of the one I grew up with in Brooklyn. It had the same problems you are facing. I highly doubt there is a radiator in this bathroom. The OP can comment if it exists or not. The large diameter steam pipe in the corner is a typical set up for bathrooms in old buildings. There is probably one thermostat controlling the heat for the entire building. The apartment above does not get to set its own temperature. How warm you apartment is in the winter is determined by what floor you live on. I agree if this is the only bathroom then it should to have a tub. I am not sure if re-configuring the tub is going to lower the resale value on a $1M+ coop in NYC. Putting up the wall between the tub and the sink makes the shower more functional. But it will make the bathroom look smaller and block some of the light from the window. I still think if you are going to move the tub the something like this one at Home Depot could work. It is 6 inches shorter than a normal tub. You will need 54 inches from stud to stud which may be possible once the plaster and lathe are removed from the walls. You could install the tub 8-10 inches away from the window wall. A shelf could be built between the tub and the wall and covered with tile. That becomes a place to hold your shampoo bottles and soap dish. Most of the steam pipe would still be exposed and will keep the bathroom warm even with the shower curtain closed. The shower head and controls stay on the same wall. This will open the space to put in a 36 - 48 in vanity with a granite counter top and a wider medicine cabinets and better lighting. That will give you ample storage space. Something that was not an issue when this bathroom was laid out 100 years ago. Have you asked any of your neighbors if they have remodeled their bathrooms? It would be helpful to get ideas and see how they dealt with these challenges.

first off, that is a horrible niche design. Cutting the tile to border the metal edging is not needed. throws off the tile design. if you want a niche, again, do the math and place it where it can fall symmetrically between full tiles. like this one. nice and neat. use a metal edge like a Schluter Jolly for the border, or see if your tile has a liner or bullnose feature. secondly,,,tile layout depends on what the manufacturer recommends. most of those tiles in that size should be placed on a 1/3 offset, not 1/2. it is because of bowing and cupping. some tiles are not perfectly flat. place two tiles back to back (or front to front and see if you see light between them or if they are perfectly flat to each other. Whatever tile you buy, they should have specs that tell you the grout width, and the way to lay them. I do like the first tile w/no offset. but if you want this one above, try for a 1/3 offset layout. there are a few ways to do it. Both of these are 1/3 offset. nice niche above, this one below, meh. should have been larger and fit within that one full tile. And watch those corners. you never want a small sliver cut. The one pictured is ok. I just dislike how they did the niche. 12x24 tiles w/a perfectly placed niche. and the tiles are finished on the outside edges. see how it fits between those tiles w/no tile cuts around it? this one too. placed perfectly between full tiles. you must do the math on a dry layout and tranfer those numbers to the shower wall, placing the niche exactly where your tiles will be laid. another excellent measured niche. full tiles above/below, no sliver tiles in the corner, the niche was bordered on the inside w/full quartz pieces and a mosaic tile on the back. very nice. Outside edging is a type of liner in that same tile design. bullnose edges would also work here