The meaning is broadly the same, but the sentences are not always applicable in the same circumstances.
“I'm sure he will make a good teacher” implies that he is currently not a teacher, and that when (or if) he becomes a teacher, he will be a good one.
“I'm sure he will be a good teacher” is similar, but applies to a definite point in time, whereas “will make” applies to an unspecified (and possibly hypothetical) future time.
“I'm sure he will become a good teacher” implies that he is currently not a good teacher, either because he is currently not a teacher, or because he is currently a bad teacher.
I'm sure he will make a good teacher, if he decides to quit his office job.
I'm sure he will be a good teacher. Let's hire him for the next term.
I'm sure he will become a good teacher, after a few more years' experience. Right now he's mediocre.
Some examples in the wild:
signs your boyfriend will make a good husband [The marriage will turn him into husband, and the question is whether he'll turn into a good husband or a bad husband.]
ways to tell if he'll be a good husband [Same question as the previous one really, but phrased differently. After the marriage happens, he will be a husband; will he be a good one or a bad one?]
will my boyfriend become a good husband? [Here, means the same as the previous two.]
Separate or stay? Is there a chance he'll become a good husband? [Here, he is already a husband, but not a good one.]
The nuances can change if you add a time complement.
I'm sure he will make a good teacher in the fullness of time. But right now, he's mediocre.
I'm sure he will become a good teacher when he completes his education degree.
“Make” carries a sense of achievement, whereas “become” sounds more passive.
In the past tense, the implications are somewhat different for make. “He made a good teacher” makes me think that he is no longer a teacher.
The only verb that means "working in a certain way" is operate; the other verbs have different meanings.
For example, implement means "to make something that has been officially decided start to happen or be used."
A new work programme for young people will be implemented.
The regulations implement a 1954 treaty.
When speaking of code, I could say "I will implement the new program features over the next week."
As phrasal verb, carry out means "to do something that you have said you will do or have been asked to do" or "to do and complete a task."
Best Answer
Note that there may be regional differences here. For example, New Yorkers famously wait on line, while most of the rest of the US waits in line. Link.
As a US-English speaker from California, I would say that "on a hill" indicates a physical location on an elevated area. For example from the lyrics of a great early Rock song, "I found my thrill, on Blueberry Hill". "On a hill" or "On the hill" are commonly used phrases. Especially if you live near a hill. :)
The phrase "at a hill" is one that I do not recall hearing. If I were to hear it, I would imagine it as the abbreviation of "at the foot of a hill." That is, standing in a place at the bottom of the hill. Another possibility is that the hill was a target. Example: "I aimed my missle at the hill."
Perhaps some context for where you saw or heard "at a hill?"