1) Nanjing is a big city - actually more than enough stuff for several days. It's the official capital of the RoC, has plenty of history (including the very dark part when the japanese brutes did the massacre of Nanjing - if you got a strong stomach, I'd strongly suggest to visit the museum) - also, it sports now an excellent public transport network, and tons of good hotels. You can do some hiking in the mountains around Dr. Sun Yat Sen memorial, visit the old sites of Pre-War Nanjing including Presidential Palace, visit the first ever YangZe Bridge built - I suggest asking TripAdvisor for more details. In short, Nanjing is less international than Shanghai, but it has a lot of history.

2) Personally I'd suggest the bus, since it's most comfortable compared to the subway, for a relatively low price. In the past I took the bus to the normal Shanghai Railway station (easier to actually change from bus to train) quite often. Alternatively, if you're not in a hurry, take the subway. It takes a bit longer, but the interchange is on the same platform (and much cheaper, of course) - Maglev+Metro is actually requiring the most amount of "changes". But all 3 options aren't THAT much different. With (heavier) baggage it would always be the bus for me, if not very much in a hurry, all by metro is my choice (did this in- and out of Shanghai in spring, found it rather convenient with light luggage, and not really much slower when the metro just drives off compared to possible waiting time for Maglev + need to change "properly")

3) Never picked up tickets in Hongqiao station. Regular Shanghai station always had an "English speaking counter" on the far right - other stations have it on another side, so no clue where it's exactly located in Hongqiao. However, I've found the setting always to be clear enough signed, never really had trouble to buy/pick up tickets. It's not much fun, though, so if I get a chance to buy tickets at a travel agency in a city (usually 5 RMB extra) I'd happily do that. But picking up tickets at a station (or even buying) is fine, outside of the golden weeks. I suppose you don't need explanation when those are.

4) 7.30pm sounds like a very safe bet to me. In fact, I'd probably say that's about the best time if you pre-book the tickets. If you arrive more or less on time, you should be out of the airport no later than 5pm even with terrible queues (or quicker if none) - giving you plenty of time to even take the metro-only connection.

5) I think the Hilton Wanda Plaza is about the WORST Hilton I've experienced in China. It's fairly new, but my experience there was beyond terrible. First room being occupied I got (not kidding), then staff who got my luggage running away, leaving me with all luggage (had plenty on that occasion) in the corridor, not coming back even after 20min - eventually I somehow managed to drag everything into the lounge.. where they were clueless, new room I eventually got was terribly stinky (non-smoking, HAHA!), second room wasn't much better but I eventually was just tired.. lounge offers were sub-standard, cheapest Tsingtao (3.1%) for example, food also less than what you'd expect. Breakfast was "ok", but nothing memorable either. No "recovery" from the hotel at all.

While the Riverside had GREAT service. (Both hotels as Hilton Gold)
Got great Riverside room (after having booked cheapest room), lounge access (with great staff and awesome dinner including "extended" happy hour since they insisted on keeping it open), the spa, while not being very new, was in very good shape with a great pool, and breakfast was fantastic. Oh, and it only cost 2/3rd of the Wanda Plaza.

So yeah, if you ask me, if it has to be a Hilton in Nanjing, take the Riverside. The Wanda Plaza isn't really downtown anyway (several stops by metro)
Riverside is quite near the (old) Nanjing Railway station. But it indeed lacks good public transport (If you know how to use Didi, it's not really a problem..)

Personally, if you'd want to stay in the city centre with good public transport, I'd pick other hotels than a Hilton in Nanjing.

But others might have had less bad experience at the Wanda Plaza and might recommend..

6) I'd plan to reach Shanghai (Hongqiao) 3.5hrs before your flight departs. That will give you plenty of time to make the flight. For the railway tickets for the return, why not buy them at Nanjing Railway station when you arrive there? Then you'd not have to worry about them anymore, their delivery, or anything. Or just buy them while in the city at one of the various travel agencies that can directly produce them.