Yes, your proposed plan is doable. You need to make sure and waterproof the window, since it'll be exposed to water spray in a shower. You mention "adding some tiles" but to make everything watertight, you'll really want to tear out what's there and start from scratch. You'll need a new shower base (either tiled or prefab pan), then the walls should be waterproofed with a paint-on membrane or kerdi, which needs to be monolithic behind the tile. Then you'd tile over the whole thing. Price depends on the materials you select and the labor cost in your area. It would be best to get a couple contractors out to give you ballpark estimates.

Will do, once I take a closer look and have a chance to draw up the layout ! Frankly this is the only picture I have and I need to take more pictures. We just removed contingencies a few days ago, so barely getting started. Would you happen to have an example of how a layout mapped on graph paper looks like?

Building code requires that you must provide access to the pump for service in such a way that otherwise permeant structure does not need to be removed or a hole through the exterior of the house not created. I forget the exact wording but you need to be able to open a panel. You can build a shower there but the access panel may be a sticking point for inspectors. Make sure to highlight that when the city does a plan check. The pump does need some ventilation but they are designed to run pretty warm. you can always put a few holes in the floor near it, is this 2nd floor or basement/crawlspace underneath?

You mention subway tile, but you do not include any pictures of it. Subway tiles come in a ton of different colors. You will get better advice if you include a photo of or link to the subway tile you plan on using.