1. I hit the chair in front of me.

1-1. I hit the chair in front of myself.
2. I hit the chair before me.
[They are okay. They are the same. By the way, do you use #1-1? A reflexive pronoun is used here.]

3. I hit the chair in back of me. [O]
4. I hit the chair in the back of me. [X]
5. I hit the chair behind me. [O]
6. I hit the chair at the back of me.
[Can we use the expressions except #4? What about #6? Do you use #6? Is #6 the same as #3 and #5?]

One is preferable. One-one is not. Two is acceptable, but not what we would say in the U.S. It seems awkward.

Three and 5 are acceptable. Four and six are awkward. They all mean the same, yes, but three or five are the ways we would say it.

3. I hit the chair in back of me. [O]

This sentence is grammatically correct and means that you hit the chair that is positioned behind you.

4. I hit the chair in the back of me. [X]
This sentence is not grammatically correct. We do not use "in the back of me" in this context. Instead, we use the word "behind" to indicate position.

5. I hit the chair behind me. [O]
This sentence is grammatically correct and means the same as sentence 3. It means that you hit the chair that is positioned at the rear or backside of you.

6. I hit the chair at the back of me.
This sentence is not commonly used in English. While it may be comprehensible, it is more natural to use "behind" instead of "at the back of." The phrase "at the back of me" may sound awkward to native English speakers.

In summary, sentences 3 and 5 are both acceptable and convey the intended meaning. However, sentence 6 is less common and less idiomatic in English.