As already mentioned, people in Japan speak English but not everybody. However, you will always find someone who will. Even if not, Japanese are extremely polite and will guide you the best way they can to help you get where you need, if they won't be able to explain, they might walk with you.
Yokohama and Tokyo are very close to each other, one train ride will get you there in about 30 minutes.
When it comes to food - you will find many great places to eat. Expensive and cheap - some places have everything explained in Japanese, but many do offer English menus. I would suggest to try them both, for the sake of experience and often the places that have listed everything in just Japanese, might be cheaper but of very high quality. My personal favorite food is Ramen in Japan, and you can find dishes ranging from 6-20 dollars. Doesn't mean 20 dollars would be better than 6 dollars one, all depends on the district and if it's designed for tourists. Here you can find an interesting ramen guide for Tokyo - http://www.sprayedout.com/best-ramen-restaurants-tokyo-japan/. Around Shinjuku in Tokyo, you will find many great restaurants and that's the area you most probably will be in Tokyo as a tourist.
Renting a car in Tokyo? A big no in my opinion. It will cost you a lot and you will waste time as well. Trains are the best forms of transportation, cheap, fast and will get you everywhere in Tokyo. That's how most Japanese people travel there as well.