Despite being taught in western textbooks, nobody really says "你好嗎？". I think they teach it because westerners find it hard to understand people not asking "how are you?" when they see each other. "你好嗎？" literally means "are you good?".
"你怎麼樣" literally means "how are you?" and is more commonly used than "你好嗎？", but still not really used that often in the great scheme of things.
Most Chinese people will say things like
你吃了嗎？ Have you eaten?
（你）最近忙嗎？ Have you been busy?
（你）最近過得好嗎？/（你）最近過得怎麼樣？ How have you been recently?
99% of the time you'll want to use 人 for person. 士 usually appears as part of largers words, such as 人士、紳士、騎士 etc.