There are so many questions there, I fear I may miss some.
First, prepositions are hard: they follow few if any easily articulated rules. When you are talking about the perspective held by a person, you can then say
the perspective of Ms. X
When you are talking about what the perspective concerns, then you can say
Ms. X's perspective on Brexit
Ms. X's perspective about Brexit
I prefer the first, but I am not sure I can articulate a reason for that preference.
Second, With respect to your examples 3/4, 5/6, and 9/10, #3, #5, and #9 are idiomatic, but #4, #6, and #10 are not. What is the reason?
As you undoubtedly know, both "the man's horse" and the "horse of the man" are grammatical and mean the same thing. However, "the man's horse" is preferred unless there is a reason to use the alternate construction.
The horse of the man is brown
is far less common than
The man's horse is brown.
However, there can be circumstances where the alternate construction is not merely preferred but required.
The horse of the man wearing the red hat
In any case, you frequently do have a choice of how to show possession with respect to nouns. It is, however, not at all idiomatic to replace a possessive determiner like "my" with "of" plus the corresponding possessive pronoun such as "mine."
Third, #7 is quite wrong. "Number of" is a set phrase.
You could use the noun "number"
The number of students present here is twenty.
Notice that the subject is the singular noun "number." Or you could use the plural verb
The students present here number twenty.
Fourth, your example #9 is grammatical and perhaps idiomatic, but without any context, it seems awkward. What sounds more natural is
He is badly mistreated.