B. permits students to cook, serve, and to buy their food.
It breaks the parallelism. Whenever we are dealing with infinitives in parallelism, it has to be
To X, Y and Z or To X, To Y, and To Z.
Only these 2 forms are acceptable. B option is like
To X, B, and To Y.
C. permits students to cook, to serve, and buy food.
Here the reasoning goes like
To X, To Y, and Z. Incorrect.
D. will permit the student to cook, serve, as well as to buy food.
This option is dicey. First there is no need to use Future tense here because the rule is effective from present. Moreover, using a singular" Student" instead of "Students" interferes with the meaning.
One more flaw in the option is omission of "and".
The last part "as well as" is an additional information. In this case there must be "and" between cook, and serve.
E. will permit food to be cooked, served, as well as bought by students.
This option is needlessly passive. Moreover, the "and" problem is still applicable in this option.