You might want to post your question on the discussion side. This is the picture gallery and folks don't really come here to answer questions.

It's a matter or personal preference, you can do either. But it can sometimes dictated by how much wall space you have or the tub style that you have selected to install. If using a vertical bullnose to contain the subway, most people will take the bullnose and just use that down the outside edge of the tub.

For a jetted tub used as a shower, it has to have an integral tile flange. That allows the wall cladding to overhang and any water that hits the wall to not go behind your walls. There aren't that many in that size that are inexpensive. It will need a specialized drain, and, if you want to spend any time in the tub, a supplemental heater so the water doesn't cool off so fast. Since it's a tub/shower, the wall cladding will need to be redone to be waterproof into the tub. It's possible, if the build is recent, and it was done with the proper vapor barrier behind it, that only one row of the tile would need to be pulled in order to replace the tub. But, I wouldn't count on that. I'd count on having to replace all of the wall cladding in the alcove. That can be as cheap as a plastic surround for around $100 or cheap tile with the proper vapor barrier for probably $150 or so. The first is the easiest and the least chance of leaking. The second will read as more upscale, but you have to be sure your contractor understands about the vapor barrier and correct materials to use to tile this (NOT mastic.) And since you have that torn out, it would be foolish to try to keep your current control valves for the bath unless they are also very new. New safety standards are in place for anti scald mechanisms. So, you will need a new shower/bath faucet and valve. Then you will need the electrical line run from the panel to the location for the whirlpool pump and supplemental heater. That location is usually opposite the drain side of the tub. You will need to be able to site an access panel that is removable to be able to get to the electrical innards here. That can be from an adjacent room, or from a hidden panel on the tub itself. All in all, you might be able to get all of the needed materials for 2-3K if you shop the box stores carefully and find some bargains. The danger to that is that if you are inexperienced, you don't know if you're buying quality or crap. They sell both. And that's one reason that it would be simpler to let the pro pick the products after you tell him the features that you want. Then you've got to pay the contractor labor to install all of that. The electrician's price will depend on how difficult it will be to access the panel and run the wire to the location. For that, it's a really good thing you are on a crawlspace! That makes it cheaper for both the electrician and the plumber. On the whole, I'd expect your project to cost between 5-7K, depending on location, and if you have no DIY skills to bring to the table and have to hire professionals for the whole job. And be sure that you hire someone that is licensed and insured to be in your home, and will pull the proper permits to get the job inspected with your code office. Some handyman guy isn't licensed to do electrical of that nature, and while he might be able to do the demo and get the tub in place and glue on the plastic surround, it's unlikely that he'll have the right insurance to deal with a large job like that, and thus probably wont' want to pull permits and be inspected. They are usually limited to smaller jobs like simple fixture replacements like a faucet or light. Which this isn't. Just remember, you are doing a project that combines electricity and water. You really have to know what you're doing here! A small General Contractor should be able to do the complete job, and also carry the needed papers. And he should have no problem with the code guys coming in to inspect his work either. If he does, then he's not the right person for the job.

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.