Youre male so your height wont be an issue.
Im 184 (I think thats around 6 foot) and I have no problems. In fact there are lots of big guys in Japan. Not as many as there are in say the US (assuming that is where you are from) but it is not uncommon to see guys my height or taller that are at least by appearance, Japanese.
Safety- Well there is nowhere that is 100% safe but in general your friend is right. Just use common sense and you wont have a problem. (Dont walk down dark alleys, go out with friends, keep your belongings well secured etc... the same sorts of things you would do anywhere)
Food- They have these things called "supermarkets" in Japan lol
Just kidding. Fresh food is easy to find. This is the country which popularised sashimi remember!
Korean- Cant really say as Im not Korean. Im at a foreign language campus so the Japanese people here are quite liberal-minded. If the university your going to is any good then theyll have good support systems and an environment which is welcoming. Outside campus I cant imagine youd have much problem either. After all there is no way to tell a Korean from a Japanese purely via physical appearance so noone is really going to know that youre Korean untill you tell them. Then I guess its up to the person. I also have Korean Ryuugakusei friends and they havent spoken of any issues.
Getting a bike is a good idea. Ride on the sidewalk though as Japanese road ettiquette is perhaps a bit different from your own country. Most people ride on the sidewalk anyway.
Peace
EDIT- Looks like Nyororin beat me to it...