a) Never having stayed in the Narita area I can't give you a better estimate, but the airport is basically an hour outside of Tokyo using express trains that run straight from the airport. I believe that staying in Narita will add two to three hours a day of commuting overhead to your sightseeing.
b+c) I had better experiences as a diamond with the Conrad, if only because the lounge and breakfast were so good. I got upgrades in both hotels, but my memory is that the ones at the Conrad were more common but less meaningful (most room differentiation at the Conrad is view and level, but all levels and views are great). The Hilton is good, but not special -- which is weird because it can sometimes cost more than the Conrad.
b2) Neither hotel is in an optimal location for transit, but I'd give the edge to the Hilton. The hotel is a 10-15 minute walk from Shinjuku station (or a short cab ride/occasional free hotel bus), and it's easy to go anywhere from Shinjuku. The Conrad is a little closer to it's station (Shimbashi), and there's a silly light rail line from there that will drop you very close to the hotel, but it's not Shinjuku. That said, as a tourist you're likely going to spend a lot of time on lines that service both stations, so it's not like the Hilton will save you loads of time each day.
d) Both hotels are in dismal business districts that aren't very interesting at night, but a bit of walking will take to you to loads of restaurants, especially if you walk to Shinjuku proper from the Hilton.