This may not be the best site for teaching-related questions overall (the Japan forum on Dave's ESL Cafe is a better bet), but I can answer some of it based on my experience. If you're going to be in a small town or rural area, I wouldn't count on being able to use much English. If you're in one of the more backwater prefectures (Tottori, Saga, Yamagata), you probably won't be able to use any at all. As for culture shock, it really depends on the person - I dealt with fairly little, but I've known a couple people that took off within a month or two of arriving because they couldn't handle it. I will say that rural life in Japan will involve a lot more than being based in one of the big urban centers like Tokyo, Osaka or Nagoya.
It's hard to comment on living conditions without knowing where you're going to be. Be prepared for smaller portions at restaurants. Don't count on being able to find clothes that fit well if you're at all larger. That especially goes for shoes. Food usually isn't an issue if you're open-minded. But then again, if you're in a really small city far away from the big metropolises, I wouldn't expect anything at all cosmopolitan. On the other side, Western and other world cuisine (well, not anything too exotic) is pretty easy to come by in the bigger cities.
Opportunities to travel obviously depend on your job situation. Most ALTs get significant time off in the summer and early spring. Those periods conveniently coincide with the jūhachi kippu discount JR pass, which allows you cheap travel on any non-express JR train. Many people use those to get around the country affordably (if slowly).
School settings will be pretty regimented and if you're in ALT, be ready to basically act as a human tape recorder. There are exceptions to that sort of work, but in general ALTs don't have much control over lesson planning or actual curriculum. Students will be obedient, if lethargic at times. Unless you're in a more prestigious high school, kids probably won't know or even be able to learn much English, so keep expectations modest. English learning is by and large only for test purposes (college entrance exams), so conversational ability is very much on the back burner.
A lot of the remaining questions I can't answer without knowing your exact destination and work situation. I will say though that if you don't get sponsored for a visa and job before arriving in the country, you're going to have a difficult time putting it all together in a small town. Tokyo and Osaka can be maddeningly crowded, but there's a good reason why most foreigners end up living and working there. And tracking down and arranging an apartment will be next to impossible on your own in a small city, as real estate agencies most likely won't speak English and you won't be able to get into a rental without a guarantor. If you manage to get on the JET program, this all will be taken care of painlessly, and rural or small town placements are quite common there (especially if you request them).
Last, regarding being a woman in Japan, the country is overall very safe, but there are certain risks for females here that males don't have. I personally go anywhere I like in the cities at any time, but I don't think I would if I were a woman. There's a significant amount of rape and sexual assault in the country, and much of it goes unreported. That said, the big cities are far worse than the countryside, so in a small town the risk is probably pretty low. Overall, the most common thing is stuff like groping or perverts swiping lingerie hung out to dry, but it'd be a lie to say that Japan is a problem-free zone for women.