网上 describes a place. in internet , online and we always add 在 in front of 网上 上网 describes a motion . surf the internet. I buy plane tickets online= 我（I）在网上（online）买（buy）飞机票（plane tickets） I surf the internet to buy plane tickets= 我（I）上网（surf the internet）买（to buy ）飞机票（plane tickets）

In general they are not interchangeable. "shang wang" (上网）is used as a verb, it means "surf the internet". For instance: what are you doing now? To answer that you are online (surfing) you can say: wo zai shang wang. "wang shang "(网上）describes the status of being online. All your examples should use this word: wo zai wang shang mai ji piao <-> I buy plane tickets online. wo zai wang shang xue zhong wen <-> I go online to study Mandarin. zhe bu dian yin wang shang mei you <-> The movie isn't available online. There are also other ways to say that you are online. Ta xian zai bu zai xian<-> he/she is currently not online. It also describes the status of being online. Usually "zai xian" is used to describe that a person is online. Also "wang shang" can be used together with other words to create a new word. e.g. wang shang yin hang <-> online banking

网络 (wang3 luo4) = The internet