Is it permissible to offer services to clients that I am not proficient in or that would take a long time to complete, then when a client requests a specific service, I, in turn, request it from someone else who provides it at a lower price? Does this require a prior agreement with that person, knowing that I do not possess any of these services? Does this fall under the ruling of selling what one does not own?

It is permissible to offer services on the site for you to complete yourself, or by paying someone to complete them for a lower wage than what you agreed upon with the requester. This falls under the category of ijara (leasing/contracting for hire), but this permissibility is conditional upon: the commitment to the lessee's conditions regarding the quality of work and similar aspects, and that the lessee has not stipulated that the shared ajir (hired person) perform the work himself without anyone else. Presumptions and custom take the place of a stipulation.