Wood – Is this water damage, dry rot, or just old age

1. Tools -- as long as you have a circular saw (and a homemade or bought rip guide), you can do this. No tablesaw, no jointer, no planer, unless you really want those. If you absolutely have to buy a new toy, consider a biscuit joiner (Porter Cable 557 is the classic, and readily available used), as that'll make assembly of the cabinet easier and yield a more solid product.

2. Wood -- it sort of depends on the look you want. If you're concerned about the window, I'm assuming children, who will 'distress' a softwood like pine over time. A softwood will be cheaper and easier to work with, though. (Maple is nice, but notoriously difficult to stain well. Birch would be an okay choice. Oak looks like oak, if that's what you'd want.)

3. Considerations -- just make it solid and it'll be fine. Build it a little undersized for the space and use the side/top to fill in the gaps. Design adjustable feet to prevent agony when you discover that your floor isn't level at the front. Google 'french cleat' for an idea of how to lock it into the back wall.

4. Upholstery -- personal preference rules here, but I'd have a separate hunk of plywood with foam and fabric/leather on top. Use a few dowels to index/locate the padding and keep it from squirming around. You could farm that out or diy it... it's not hard, though you have to work a little at getting the fabric stretched nicely. The price will scare you, but I'd go for high density foam for durability.

5. Windows -- I think the extent to which this'll be a problem depends on the exact location of the windows and the inhabitants. If it becomes a real problem, you could screw plexiglass in front for protection.

6. Design -- this is simply a cabinet with different proportions. Start with a separate base made of 2x4s that you can level. (Perfect studs matter here... take the time to pick nice and dry ones.) Then it's just a box (I suggest birch-faced 3/4" plywood; no need to go to town with baltic birch, though) with a base, 2 sides, hopefully a central support or two, a top, and a solid back. (Typical cabinets these days have a flimsy back panel; I'd recommend something more substantial, like 3/4" ply.) The aforementioned french cleat will tie it to the wall. Depending on the visual cues elsewhere in the house, you can leave the front plain or dress it up in various ways. (Google 'applied molding'.)

7. Feasibility -- you can do this. Absolutely. Positively.

It's hard to tell what that is but I would not worry too much. If it was from a water leak I would think that you would see discoloration down along the bottom, along with actual swelling of the particle board. That, along with your statement that there are no other signs or symptoms, make me think that could be a dirty smudge left by the hand of a carpenter, painter, installer, etc.