I went to vote today.

* "the right guy to vote for" is a nice, stylish way of saying it. A more simple and straightforward way to say it is "I found someone who I could vote for."

**  "Sang" versus "Sung" - "Sang" is simple past tense. "Sang" is a participle that needs to be preceded by an auxiliary verb ("they had sung" or "she will have sung"). You will rarely need it, so generally, stick to "sang." (Sorry English verbs are so complicated).

*** "his opinion is strong and dependable . . ." Not very clear. Maybe "he has big ideas and integrity. . ." For opinion, I think you mean his values and/or his platform (the things that the politician believes in and promises.So "he has big ideas" or "strong values" or "a positive platform" would work. "Integrity" means that he is honest, and does what he promises to do. 

I went to vote today.

(good)

(ok, but I'd say "Today was election day in Japan." instead)

Since I'm not interested in politics, I don't really go to vote.

(Since I'm not interested in politics, I rarely vote.)

But this time, I found a right guy that I vote.

(But this time I found a candidate that I can support)

He is a musician and totally different from other candidates.

(good)

He gave speeches some area in Tokyo and there were some musician who supported him and they sung songs before his speech.

(He gave speeches in Tokyo and some of his supporters who are musicians played music and sang before them)

The atmosphere was like a concert. But his opinion is strong and dependable so many young people who were not interested in politics endorse him.

(The atmosphere was like a concert, but his opinions are good and he seems dependable so many young people who were not interested in politics before will support him)

I hope he change Japanese politics.

(I hope he changes Japanese politics)