I take it you will arrive at the terminal designated for cruise ships. If this is the case it is not a very long taxi drive. The distance to the A-bomb area is roughly 5 km. Depending on traffic it will take you about 20 minutes to get there. Enjoy your trip.

Seats are reserved for hibakusha and their families by invitation. You can join the event, but I don't think you have a seat.

It depends. Ask beforehand. BTW, there is no onsen at Nagasaki Peace Park.

We were on a cruise ship and used the trams for our transport. We are both in our 70"s and did not find the trams a problem. Inside the Cruise Terminal information staff will give you maps and tell you where to get the tram. We started by visiting the Peace Park and then walked down to the Atomic Bomb Museum (through the Hypocentre Park). We then visited the one legged Tori Gate and then Sofukuji Temple. All this was done on the tram and short walks. The tram routes follow a colour code like MTR routes - easy.