my personal points of view are in brackets.First you never say positive quality for a quality is already positive.so:
"One quality i have is to be a very compassionate person"(you can keep sympathetic but compassionate is more common)
"Other people problems", "i can deeply feel and understand other people problems"; " i am always willing to help homelesses, old and famished people who are often sitting or walking along the streets( for you canīt sit along the street), or anybody else in a desperate situation(sounds better)." sitting in the street". "i felt so much sympathy that i gave her...". " having this kind of character" (or you can keep personality but donīt add trait)." do not want any help from others"; "solve their problems"; " i love this quality and I am pleased to impart it to all my friends.."