Do 向 and 学 or 学习 work together here？
1) 一心向学, means single-mindedly study. Here, 向 means 'towards', or 'head for', or 'point to'. 学 is a noun here, means 'study'. The phrase is a Chinese Idiom (成语), and the usage is kind of classic Chinese (文言), a little different and simplified from the modern usage. 

2) 向有礼貌的人学习礼仪. 向 somebody 学习 something, means learn something from somebody. 向 means 'towards' here too. The meaning is like, turn to somebody, and you learn something (from him).

Sorry for my poor English and I wish I made that clear.