I went to vote today.

(good)

It was election day in Japan today.

(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)

"nightclub" is correct for an evening drinking establishment. If you separate the words it can imply other meanings, e.g. "He used to have a black stick he called a 'night club'"

Person A -- good Person B -- The first line should be "He wouldn't have gotten married to you anyway". The second line is good.

These are all generally correct. The line "I haven't any money with me." actually can be used, but it implies the "got" and I don't know anyone that would say it like that. Most people would simply say "I don't have any money" or "I haven't got any money" as the "with me" implies that you have money, just not currently with you.

Lol - most people I know would call it "the handle thingy" or something just as foolish. There is a specific name, of course, but most people don't know it. We'd generally just say the "window latch", or "window opener"

Yes, although most English native speakers would ask "Are you still hiring workers?"

I have back pain again.

(good)

When I picked up a stuff from the floor while working, my back pain came back!

(While working, I picked up a load of stuff from the floor and my back pain returned)

I didn't feel any pain recently,I was careless at that time.

( although I don't feel any pain now, I was careless to hurt it again at that time)

Since I didn't want it to be worse, I had half day of in the afternoon.

( since I didn't want it to get any worse, I took a half day off from work that afternoon)

I hope it get better soon.

(I hope it gets better soon)

Cramp

I had a cramp with my right leg when I was sleeping last night.

( I had a leg cramp while I was sleeping last night)

I have a cramp with my leg while sleeping once in a while.

( I get them once in a while )

I know how to fix it but it was strong one last night so I had pain for a couple of times.

( I know how to fix them, but they were strong last night and returned a couple of times)

Finally I could relieve my pain and I went to bed again.

( They finally relented and I could sleep again )