If your living space is ground floor only, a deck - typically an elevated outdoor structure - doesn't make a lot of sense. The architecture of your living space just does not accommodate that. Why not just a paver patio with a more generously sized stoop?

There's a lot of space not under the staircase that you can put a deck...but honestly for first level access I would consider a patio instead. They're much less expensive, don't provide homes for critters, and seamlessly tie into yards. Our neighbors actually ripped out their first floor back deck and put in a patio instead, for many of these reasons.

Would you pave the patio right up to the building or would you start it in front of the stairs?

The area under the stairs is never a pleasant place to sit, I would close that in with some sort of lattice with doors so you can have accessible storage

It is really your choice....with some consideration for materials as well :-) Proper slopage, drainage and waterproofing are more easily addressed if you do leave a space (which can then be planted) or it can be built right up to the structure, given those considerations as well.

Personally I would put the patio from the stairs out. The space in between the patio & structure should be planted and sloping away from the house for drainage (and aesthetics).

If it is designed and installed correctly, there is no reason the patio could not extend right up to the structure.....if that is what you want. I'm not sure aesthetics are really a factor in that decision :-) They are not predefined but a matter of personal choice.

I would also consider an awning, sun sail or umbrella(s) to block the view from above.

Where do the people upstairs enter and exit the stairs?