1. Both “cost of filing an application” and “cost for filing an application” are correct usage, but they differ in terms of point of view. The “cost of filing an application” refers to the intrinsic amount charged for filing the application from the standpoint of the entity collecting it, as in “In our school, the cost of filing an application for library privileges is PhP500.” On the other hand, the “cost for filing an application refers to the filer’s out-of-pocket expense in filing the application, as in “To me, the cost for filing an application for library privileges is PhP500.”
2. Both “this elevator stops at every floor” and “this elevator stops on every floor” are grammatically correct, and it would be difficult to explain a semantic distinction between the two usages. However, by convention, “this elevator stops at every floor” is much more widely used than “this elevator stops on every floor.”
3. Prepositions are used on a need basis depending on the phrasing of statements and the type of sentence construction. Note that the sentence “Each team was allotted fifteen minutes to come up with an original solution,” where the preposition “to” is used in the complement “to come up with an original solution,” is actually equivalent to the sentence “Fifteen minutes was allotted to each team to come up with an original solution,” where the preposition “to” is used to link the object of the preposition, “each team.” (This latter sentence can even get rid of the preposition in this elliptical construction, “Fifteen minutes was allotted each team to come up with an original solution.”) What this means is that the English language allows for flexibility in the usage of prepositions, in keeping with their grammatical role as clarifiers of the meaning of statements.
The thing to remember is that functionally, prepositions are tacked on to a noun phrase so it can be properly modified or elaborated on when forming a sentence. In particular, in your second sentence, “Management reserves the right to allot to each employee the work he or she is expected to do,” the preposition “to” is actually part of the infinitive phrase “to allot to each employee the work he or she is expected to do,” which serves as object complement of the sentence. Strictly speaking, therefore, "to" in that sentence is not working as a preposition but as an integral part of the infinitive "to allot," which is actually a noun form.
