The hospital

I'm in the hospital. Yesterday I had succesfull surgery. The doctor removed a metal pin from my leg. Now I'm staying in the ward for the postoperative examination. My neighbor in the ward is an old man who always speaks about everything.

("talks about everything" sounds more natural)

He discusses about the medicine, the weather, the politics, the economics, the last (latest) news e.t.c. Sometimes that ("he" sounds more natural here) is a little annoying, I try be polite and patient.

Elderly people are in need of attention.

Or: Elderly people need a lot of attention.

I hope I leave the hospital after four days. I miss my family although they attend ("visit" sounds more natural here) me everyday.

The hospital

I'm in the hospital. Yesterday I had a succesfull surgery. The doctor removed a metal pin from my leg. Now I'm staying in the ward for the postoperative ward examination. My neighbor in the ward is an old man who always speak talks about everything. He discuss talks about the medicine, the weather, the politics, the economics, the last news etc.  Sometimes that is a little annoying; I try to be polite and patient. Elderly people in need of attention.
I hope to leave the hospital in four days. I miss my family, although they attend visit me everyday.

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This is pretty good. Most of the suggestions are to make it sound a little more natural. I also added a semicolon. "Sometimes that is a little annoying; I try to be polite and patient." You can either make this two different sentences: "Sometimes that is a little annoying. I try to be polite and patient." Or, since the two sentences are closely related, and when speaking you would probably say them in a connected way, without a full stop between them, you could write it with a semicolon. Either way is OK; I just like semicolons.

I hope you feel better soon, and that the surgery went well for you!

successful (adjective)   I had successful surgery.

successfully (adverb)    The doctors successfully removed a metal pin from my leg.