Let's take the answer from the explanation of this site. Though I remember there was an expert in both Japanese and Chinese. mine would not be a far away from his.
I assume questions in your question .... etc are equivalent with the the meanings of the below from the above site.
ウ: 「To denote accuracy, the center」（ Ex:Right in front, In the middle of the night )
エ：「perfect」, 「mixed with impurities」( ex : purest water, pure white )
In the case of direction
Please take a look at the below picture which I made with Excel, and please take it as 3 dimensional.
These 6 stands for direction.
In English, the below 6 words denote directions as is defined above as ウ. I would like to explain using the above picture.
The "center" is either yourself, or someone else, or something else. The matter is if it is objective ( = yourself ) or subjective ( someone else, itself ( as if you are watching them from outside )), I would like to explain with the former, yourself.
right in the middle of yourself
right ahead of yourself
right behind yourself
right above yourself
right beneath yourself
right beside yourself
The matter in concern is if what you see at is at "right ahead, or right beneath" etc. As I marked ×真ん前（まんまえ） or ×真下（ました）, they should not be slanted. In the case of yourself, the object you see at 真下（ました） must exist just right straight beneath yourself. ( even 1 or 2 degree adjustment is not allowed ( strictly speaking )) Now, 真ん中、right in the middle of yourself, when what you see at in the middle of yourself ( for example. your belly ), it exists at the same position of yourself.
He is just right ahead of me.
Here, he, must be right ahead of you. ( even 1 or 2 degree position movement is not allowed ( strictly speaking )). But in reality, there will many cases that he would be at about 10 degree right side from right ahead, so virtually, it it up to how you describe.
中, 前, 後ろ, 上, 下, 横 (**)
They are respectively as I explained above
middle, front, behind(back), above, beneath(below), side ( either left or right unknown )
Pure ( entirely ) white, Pure ( entirely ) red.
from the above definition エ.
Is there a common way to understand the usage of 真 generally?
I don'think so.
Because as I quoted above definitions, they are different. ( But the nuance, both meanings, "accuracy", "pure" have common ( or near ) semantic meanings ( in my opinion )).