I know of many verbs that can be expressed as a single character or two characters (i.e. 说 & 说话). The issue is that I don't know when it is appropriate to use one of over the other. Is it dependent on the subsequent word? For example, "我吃米" and "我吃饭面包"? Or is it the other way around? Neither? Personal preference perhaps!? I've read that there is a natural tendency in Chinese to minimize the number of characters in compound words. That being the case, should I avoid using the two characters versions entirely?
I'll try answering this (but be aware I'm just a learner).
The given examples are transitive vs. intransitive verbs:
He says hello
Why do you speak that way?
We can alternatively think of 话 (noun) as what is being said (说).
Again, we can alternatively think of 饭 as the object being eating (吃).
(I also note that both 说 and 吃 can be used as intransitive verbs, e.g., 你别说了 and 他什么都没吃.)
学 vs. 学习
In this case, which do we choose? See this question: What's the difference between 学 and 学习? It's somewhat a matter of preference, circumstance, etc.