"Are they any laws that prohibit homosexuality?" Having homosexual partners or running gay bars are not illegal if that's what you're asking.
"What type -- if any -- anti-discrimination laws exist?"
If people discriminate you for your homosexuality (not employ you, not rent you residence etc.), you can sue them and if you win you can get loads of cash, if that's what you're asking.
"Can a homosexual couple adopt children? Can a homosexual couple marry?"
I'm afraid not, but many couples live together.
"How is homosexuality approached by the majority of the public?"
You've answered it yourself. The media features them possitively in a way, gay bars are popular even among healthy women...The most homosexual-friendly place in Japan is the Shinjuku 2-chome district in Tokyo. Very friendly. But there are people who just can't help thinking it's disgusting. In the conservative countryside, things can be a bit tougher and many hide their homosexuality even in the cities.
"I am only sixteen, so I am particularly concerned with that of my generation, but any information is helpful and much appreciated."
It depends. Frankly speaking, I'd say most teens probably would find it "weird". But then in boy's schools (or girl's schools) gay has not been that rare, and they would even be relatively open. In any case, the Japanese generally do not speak loudly about their love life. Kissing or hugging in public is considered impolite. So you can remain "humble" about your homosexuality or bisexuality or any kind of sexuality outside your home until you find a friend who can understand you.