Vegetarian? You’re ****. Just give it up for a month. Seriously. Or else be prepared to source and cook basically all your own food.
You can find veg tempura in plenty of places, from what I remember, plus you get rice everywhere. Tofu/bean curd is pretty common too, although if you’re being strict then watch out for the sauces. There appears to be plenty of info online about eating veggie in Japan, so no, you’re not ****.
Your rail pass should get you on any JR (Japan Rail) run transport, which includes ferries. We used ours to get over to Miyajima (great place). And while there is an underground in Tokyo which your pass won’t work on, I found that I only needed to use it once in 4 days there since the overground JR trains got me pretty much everywhere I needed to. I used an app called Japan Trains. It was free and by the sounds of it did all the things that Hyperdia does – incredibly useful!
I took a prepaid credit card and could only get cash from the 7/11 machines. I did use my card to pay for things a few times, but yeah, mostly used cash. And lots of it; it’s an expensive place!
It’s a brilliant place, would love to go back :)