I was recently asked by someone to fill out paragraph answers for their application.
Am I halachically permitted to do so?
If they are asking you to provide the answers for them you may not do that, and for a number of reasons. It is helping someone do an aveiro, which is forbidden.
What she is doing is genivas daas, because she is fooling the school into accepting the person although they would not do so, because she is not on the level that they want, and they wouldn’t otherwise accept them. Besides that you are helping someone not be honest.
Aside from this, being that according to law it is illegal, it is also forbidden by Jewish law, as we are obligated to act according to the law of the land (dina d’malchuso).
Ch:M 328-6, Yam Shel Sholomo B:K 1-14 that dina d’malchoso applies to bein adam lechaveiro. Igrod Mshe CH:M 2-30, Shevet Halevi 10- 163, Titain Emes L’Yackov (R’ fish)pg. 331-333.