Question: What exactly is a class? Is it the period of time of one subject? Is a subject a class? Is class a group of people or is that a grade? Is a grade a level or is it an ABCDEF in the score? I have a feeling the English language is left with "class" and "grade" for all terms. That might not be true because I might be missing the true names of these things.

So how do you say these?

* People who are being studied things
* A subject
* An ABCDEF
* A place where people study
* A period of time during which people who are being studied things sit and learn

Answer: 
Your wording "people [...] being studied things" is non-idiomatic. If people are being studied then someone else is trying to learn something about them. From context, I think you mean people being [*taught*](http://www.oxforddictionaries.com/us/definition/american_english/teach) things. That indicates that someone is trying to instruct the people in question ("taught" being the past tense of "to teach").

[Merriam-Webster](http://www.merriam-webster.com/dictionary/class) gives these four meanings for "class" in school context (along with several others in different contexts):

> 
> a : a body of students meeting regularly to study the same subject
> 
> 
> 

Example: "My Biology class dissected frogs today." Perhaps this is what you meant by "People who are being studied things".

> 
> b : the period during which such a body meets
> 
> 
> 

Example: "Turn off your cell phones during class." This seems to match your "period of time during which people who are being studied things sit and learn."

> 
> c : a course of instruction
> 
> 
> 

Example: "I need only four more classes to graduate!" This is similar to a "subject", and in some circumstances and localities the two might be used interchangeably.

> 
> d : a body of students or alumni whose year of graduation is the same
> 
> 
> 

Example: "This bench is a gift from the class of 2011." This one is not among the terms you asked about.

You also asked about "An ABCDEF", which would be called one of a "grade" or a "mark" in most English-speaking locales.

"A place where people study" could be a "classroom", but also many other things ("study hall", "library", "study", "bedroom", and many more).
So how do you say these? In Australia... (not sure if you'd find this interesting at all, but any way). A lot of terms also differ depending on primary/secondary or tertiary education.

People who are being taught things are *students* (for both Primary/Secondary & Tertiary)

A subject is something like mathematics, English, history, calculus, etc. They are the same for both primary/secondary and tertiary.

An ABCDEF is known as a grade for both primary/secondary and tertiary. However while school is scored as A-F, tertiary is scored on a 1-7 scale (with 7 being a high distinction, and less than 3 being a fail) and known as a grade, hence the term Grade Point Average (GPA).

The place where people learn, would just be the classroom at school. At university, we have different names depending on the function of the room, such as *lecture theatre* or *tutorial room*. 

A period of time during which people who are being studied things sit and learn is known as a class (for both school and University).