Well, you assumed wrong. IMO, Tanaka either has just poor enough English (no surprise) that he can't make his point clear, or he is sly enough to try something to avoid his own legal responsibilities
You don't need a visa for sightseeing (unless you want to get a working holiday visa, which you aren't old enough for just yet).
You do need a visa to be a student, whether in high school, university or a language school. That is the purpose of your being here, so that is the reason you need the visa. Just because Tanaka says otherwise doesn't mean it's true. He may have to pay in order to register his school as eligible for sponsoring visas, and to avoid that he may feed you this line. It would also mean he probably doesn't have to pay certain taxes. I don't know.
You think getting a visa is a hassle? Get real. It's a legality. Don't like it? Don't come. The visa is good for 3 months and you want to study for 1/3 of that time. What a deal, eh!
No.
By the way, can you actually provide the documentation needed for the student visa anyway? Basically, you have to prove you have the funds to defray all costs of the course tuition. Only then can you be considered for the visa.
By the way, it's 2am in the UK. What are you doing up so late?