This does not make sense in English !!!
Why is 'Níl pearsanta e' wrong?
You use that structure with the copula, which links two nouns. This is linking a noun and an adjective.
The copula can be used with predicative adjectives only in limited circumstances, and the negative of is is ní, not níl.
What does the word personal mean in this context?
O' Dónaill 1977 gives "personable" which is reasonal enough, but "personal"?
He's my representative, but he's not personal?
Personable seems to be the correct English word, here.
Why does this sentence use 'tá' instead of the copula? Surely the sentence is equating something with something else?
What are the somethings that are being equated? "personal" isn't a thing - you can't have "a personal" or "the personal".
pearsanta is an adjective, not a noun.