When you mentioned a window in the shower, I was picturing a wooden framed window lower down. Yours looks pretty good. FWIW, if you mess with it, you don't want it perfectly level. You want the sill to end up sloping slightly towards the tub so water will drain down and not sit up there.
Tile is definitely an upgrade, but it is also labor intensive. If you're updating this to sell, and prefab surrounds are common in your neighborhood, it would be a heck of a lot easier.
If you can find a manufacturer name on your tub, try to stick with them. Not all whites are the same. An American Standard surround may not match a Kohler tub.