Have fun at at the Tokyo
Disneyland Hotel! Its a beautiful hotel with a great location. About your questions:
When I stayed at the Disney Celebration Hotel Discover, they offered us the tickets you mention, the 3 day park hopper. I passed on it as it was more expensive than the regular 3 day Magic Access ticket that is also sold at the hotel. The 3 day Magic Access ticket, where you name which park you will visit on day 1 and 2 and can park hop on day 3 (and 4 if you got a 4 day ticket) is currently 17800 yens while the hotel exclusive 3 day park hopper is 19400 yens. The extra 1600 yens was not worth it in my view because the parks are big enough and busy enough one day at each is good to start and then on the third, we started at Tokyo DisneySea. We rode Journey to the Center of the Earth, Indiana Jones Adventure, Sinbad, met some characters, then hopped on the monorail and finished the day at Tokyo Disneyland for food, fireworks and the Main Street Electrical Parade Dreamlights. I would not approach Tokyo Disney like Walt Disney World and do constant park hopping.
Those tickets can't be purchased in advance and have to be bought either at check-in or during your check-in at the Welcome Center at Maihama Station if you do it there.
Your next question about getting fast passes early or show tickets before your trip is only through a package as you noted. The Fast Pass system was like the old one at Disneyland and Walt Disney World, but is changing in a few days to a mix of phone application/fast pass machine all done on the same day at the park. It will be first come, first serve once you enter the parks. Alas, the Tokyo Disney app is only available in Japanese and requires a japanese language Disney Japan account. Until an english language application is released, you can obtain fast pass by arriving early at the park and going to your first attraction and registering at the fast pass machine with your park ticket. You will then get a reminder ticket and scan your park ticket at the ride you picked fast pass entrance to gain access.
For the show lottery, there are still locations around the park where there are machines where you pick a show, a time and then it tells you if you won a seat.
One last thing you didn't ask, but I feel you should know: Magic 15 Entry. This replace Extra Magic Hour at WDW and it works like this: one turnstile at each park will open 15 minutes early for Tokyo Disney Hotel guests. Once you enter the park, one or more attraction along with a limited park area will be open for you. At Tokyo Disneyland until Spring 2020, it changes due to entrance area construction. The special turnstile opens 30 minutes in advance and you can then enter Tomorrowland using your Magic 15 ticket to ride Buzz Lightyear/get a fast pass for it or get in position for Monsters Inc. or other rides. At Tokyo DisneySea, the turnstile opens 15 minutes in advance and then, Tower of Terror, Toy Story Mania! and Soaring Fantastic Flight will be open during those 15 minutes. One thing to note is that even if you check in early, you can't use it on the day you check in and can use it on the day you check out.
