The GIRM states that "these or other similar words are acceptable."

[japhy]

Are there any guidelines or rubrics specifying the form or content of the Prayers of the Faithful?

Not much. The English Order of Mass (p. 369) has a couple sentences about them: they follow the Creed; the priest presides, giving a brief introduction and an invitation to prayer; the intentions should be announced by a deacon, cantor, or other person; and the priest should close with a concluding prayer. There are many formulas/examples given (pp. 992ff).

The Latin Missal is much briefer in the Ordo; there’s a single sentence, rubric 20, which simply says “Deinde fit oratio universalis, seu oratio fidelium.” Appendix V of the Missal has formulas/examples which, at first glance, are the basis for the English examples.