In this post, we discuss the differences between 学 and 学习.
学习：xué xí [v] learn, study; follow the example of
A). xué [v] study, learn; imitate, mimic
B). xué [char] subject of study, branch of learning (suffix); school, college; learning, knowledge
1. First of all, 学习 does not share the second meaning of 学 -- 学 B).
2. 学习 can mean "follow the example of"; 学 can mean "imitate, mimic". In these two meanings, they are not interchangeable.
3. When it comes to combination among words, it has something to do with how many syllables the verb has.
3a. Modifying a noun:
学习经验、学习成绩、学习能力、学习方法: In these examples, 学习 modifies the noun that comes after it; we cannot replace 学习 with 学.
3b. Followed by an object:
学 can be followed by monosyllabic or duosyllabic objects; 学习 is only followed by duosyllabic objects:
学画: Here, 画 is the object of the verb 学. We cannot replace 学 with 学习, which means we cannot say "学习画".
学习知识／学知识，学习汉语／学汉语: 学习 and 学 are interchangeable.
4. In Chinese idioms, where 学 appears, it cannot be changed by 学习. Idioms are set phrases.