My itinerary in China: Beijin, Xi'an, Lhasa, Chengdu, Guilin, Wuhan, Huangshan, Shanghai...30 days

Hello, I will arrive in Beijing from Seoul on September 20th, 2018. Then, I will follow the route mentioned above, in that order. I read that I will need special permit to enter in Tibet. I am a solo traveler and hold Peruvian and American passports. Questions:

1.- Will I request the permit to Tibet at the same time that I request the Visa to the mainland China? I am planning on doing it at the Chinese Consulate in Fukuoka-Japan, next week.
2.- At the time of requesting the Visa to China, Do I need to show proof of all the domestic transportation to the Chinese consulate, in Fukuoka?
3.- Any other suggestions for this first time traveler in China?
Thank you for your attention,
Wilfredo