Hey! I have been on the bullet train, and it does have some tunnels. But they don't last too long. And it's just like a normal train, except a bit faster? You also have a bit more leg room. You'll see some Japanese families make it into a bit of a ritual, bringing lunch boxes and playing Uno or other card games. Also, you'll probably see other families just relaxing and playing 3DS' or watching stuff on a tablet! If you've been on a train in the UK you won't be too surprised! Look out for Mount Fuji on the way to Tokyo/Kyoto though!
Have you let your host family know about your special eating requirements? Because vegetarianism isn't as widespread in Japan as it is in the UK/America. I am positive you will be able to get rice... however, I have only ever heard of one Ramen restaurant in Japan that has a vegetarian variety in Japan. A lot of the soups are pork broth... If you're in Kyoto you should check it out, it's called
Ippudo. Your host family should know it! Also, upon googling Ippudo a few more hits came up for vegetarian ramen, so you should be fine! Just be aware that special dietary requirements in Japan are a bit of a mystery at your everyday, typical restaurants. You should be prepared to go out of your way, and spend a little bit more cash, to meet said requirements.
Your host mother might make lunch boxes for you, and cook dinner so you might not even have to worry about eating out! Just make sure your host family is fully aware of your eating habits!
It wouldn't be a bad idea to bring some food that you know you can eat, just in case. I showed a couple of vegetarians/restricted diet people around Japan a while back and they brought a lot of breakfast bars which really helped them out in the end.