Question: Is the order of the verbs important in relation to the placement of the negation? i.e. Is नेहा जा नहीं सकती as acceptable as नेहा नहीं जा सकती ?
Both are right.
नहीं is sometimes written after the verb to emphasise the negation.
Cannot ..one word
Does this mean Neha isn't allowed to go or that she isn't physically able?
It can mean either of those things.
नेहा नहीं जा सकती है is really wrong
It is not wrong. The है is optional but including it is not incorrect.
Why is राज गा नहीं सकता correct but नेहा जा नहीं सकती wrong? The correct answer given has the नहीं before जा.
नेहा जा नहीं सकती should have been accepted. You can report if you see the sentence again.