Japan 12 day schedule and questions

Hi everyone, just a question about my schedule for 12 days. I'll be in Japan for the first time with my younger sister and was wondering whether I could get some insight into:

1) Whether it is better to stick with purchasing transportation tickets on the go rather than JR pass
2) Whether the schedule is too packed or your thoughts
3) Is it safe to bring a large amount of cash with me? (We are planning to take $4k with us in cash so $2k each. I've also saved another $2k in my travel card). We will both be wearing one of those hidden money belts to carry the cash around but also leave a certain amount $100 everyday in our wallet to pay for things so people don't see us carrying a belt underneath. Should we leave the big sum of cash in our accommodation instead? We are staying at a hotel and an apartment.

DAY 1: (Arrive in Osaka at noon time)
Dotonbori to eat and walk around

DAY 2: (Kyoto)
Golden Pavilion
Kyoto imperial palace

DAY 3 (Kyoto)
Higashiyama and Gion district

DAY 4 (Kyoto)
Day trip to nara deer park

DAY 5 (Kyoto)
Day trip to Himeji castle and then to onsen

DAY 6 (Tokyo)
Travel to Tokyo hotel and free time to do whatever

DAY 7 (Tokyo)
Day trip to yokohama ramen museum and China town

DAY 8 + 9 (Tokyo)
Tokyo disney land since we've never been to disneyland before

DAY 10 (Tokyo)
Shibuya and Harajuku shopping

DAY 11 (Tokyo)
Shinjuku shopping

DAY 12 (Tokyo)
Return flight to Australia

1)
Regular oneway train(Shinkansen fastest) ticket enough for to Tokyo fr Kyoto.

2)
No.

3)
Buy good wallet with chain enough.
Japan is not so dangerous.
Or get the major international brands Credit Card.
https://www.ana.co.jp/cont-image/common/logo/0058-lang-multi.jpg

4)
No "USJ" in Osaka also Aquariums in Osaka/Kyoto?
D7 why going to China town in Japan?
D10,11 is very close no need for two days.
Open Google map.
If sister is not pretty young "VenusFort" in Odaiba may good.
http://www.venusfort.co.jp/multi/index_e.html

I wouldn't have all my cash on me & leave all but that days in my locked luggage at the hotel. Japan is absurdly safe so I never worry about it. Otherwise your itinerary looks fine, not too packed plenty of scope to do adjust as the mood takes.

I wouldn't bring that much cash on you at a time. Japan is a very cash based society, though a lot of people use IC cards.

I would consider basing out of Osaka rather than Kyoto, and daytrip the two days to Kyoto. Both Nara and Himeji are closer from Osaka, so that balances out with the time it takes to go to Kyoto from Osaka. But Osaka is a lot more interesting at night.

As others have said, it's perfectly safe to be carrying around a lot of cash; the risk is really just that you might set down and forget your wallet or purse somewhere (and even then the odds of you finding it where you left it, or getting turned in to the local police station/lost and found completely undisturbed is very good.)

If you already exchanged that much cash and own a money belt, then you might as well bring them. I feel safer with money belt than stashing it in the room. Otherwise, I personally use ATMs at Seven-Eleven or Post Office and cash 50000 yen at a time as needed (the maximum withdrawal amount depends on your bank). Your itinerary looks very reasonable at a relax pace, so you may want to research more places to visit, in case you are left with lots of time and run out of ideas in Japan.

In case you are left with enough time, on day two in Kyoto you can add Nijo castle to the plan. It is very close to the Imperial palace.
But your plan looks really good and with no rush. The above suggestion is not to make you rush from place to place but just to keep in mind in case you have the time.

Thank you everyone for your kind replies. I have changed my schedule a bit so now I will be visiting Shinjuku on Day 8 when I arrive in Tokyo (for 3-4 hrs) and then go to Venus Fort + Oedo Onsen Monogatari on Day 11 (instead of Shinjuku on day 11).

I'm also going for the maiko make over package (which I already booked) in Kyoto so it will take an additional 2-3 hrs during Gion/ Higashiyama.

I don't know what dates you're traveling, but don't do Harajuku on weekends! The crowd is insane. Its atmosphere is hip and young and vibrant, but I much prefer Ikebukuro for (girly) shopping. So many more cosmetics shops and more space on the streets to spread out. Sunshine City has everything you need! On a Sunday, I left Harajuku and felt I could breathe again when I got to Ikebukuro.

Unless you want to see or be part of the hip young crowd. Honestly, Harajuku is a lot more fun on the weekends.