Reservations opens 5 months before or 6 months for packages. The packages include hotel, some meals, tickets, and extra Fastpasses (for a significant upcharge compared to booking separately).
How tough it is to get reservations depends on the hotel/type of room and if it's a busy time at TDR. The MiraCosta is very popular, the harbor view rooms are especially hard to get. To add to the angst, sometimes there are issues with foreign (non-Japanese) credit cards going through.
If you want to know if the time you're thinking of going is busy, here's the Japanese crowd calendar (use Google translate):
www15.plala.or.jp/gcap/disney
And if you want more details about it, here's a great article:
tdrexplorer.com/tokyo-
disneyland-crowd-calendar
The Imperial Palace, you would take the train to Tokyo Station, which is less than 20 min from TDR (Maihama Station) and direct. From there, you could take another direct train (~15 min) to Shinjuku. If you plan to tour Tokyo proper for a few days though, you may want to move to a hotel in Tokyo. The two sites you mentioned are fairly convenient from TDR, but other places may not be. Here's the site I used to check train times/routing:
www.hyperdia.com