Climbing mount Fuji on September 16th

Hello,
I am planning on climbing Mount Fuji on Sept 16th on my own (as I am travelling solo). I am aware that this is off season. Would someone please answer me the following questions:
1. Do I need a permit? If so, do you know please where can I get it from?

2. I realize that there are many ways/paths, is Fuji Subaru 5th station the most convenient at the off-season?

3. I plan on climbing and descending on the same day. Is there any route in particular that you would recommend me in order to be able to return to Tokyo on the same day?
I would be very happing taking a train or a bus very early on wednesday the 16th, arrive at the bottom and climb and come back on the same day. Would you suggest me taking a particular path in order to be able to go back to Tokyo on the same day?

4. I have seen that there is a webpage to purchase bus tickets, but the dates stop at sep 10. Do you know how can I purchase the tickets in advance?

5. Besides good foot wear and warm clothe, food and water, is there anything else that you would suggest bringing?

Thank you so much! As this is a very special project to fulfill, I appreciate all the help.

1. No, but recommended to check in with the police station.

2. I climbed the Fujinomiya trail, so I don't how convenient the other trails are in the off-season. I went in the off-season, but it was in June. There was a lot of snow last year, 2/3 of the hike I had to wear crampons. Public transportation is limited during the off-season, so what I did was a midnight hike. I got to the 5th station in the late afternoon and started hiking at night to see the sunrise. In the mid morning I took the first bus back to town.
You should look at the bus guide here, it's pretty informative on the public transportation system to the 5th station. http://www.japan-guide.com/bus/fuji.html
For example, if you take the Gotemba station to Subashiri 5th Station if you start hiking at 8:35 are you able to get back to the trail head at 17:00. Can you go up and down in 7:30 hours? It's probably doable because it took me 10 hours with the snow.

3. I don't know anything advance ticket purchase. I went to the bus station next to the train station and purchased my round trip ticket. I was the only person on the bus. On the return there was only 1 other person on the bus.

4. Sun screen, sunglasses, lip balm. I got wind/sun burn on my lips.

One of the off-season regulations

" 2. A Climbing Plan must be completed and submitted "

http://www.fujisan-climb.jp/en/risk/guidelines.html