an agreement can be verbal or written; there are many good reasons for documenting agreements in written form and having each party sign the agreement
a client is anyone who needs your assistance; your client could be external (someone from outside your organisation) or internal (someone from inside your organisation)
a document outlining your understanding of the client’s needs
technical support can take many forms; this could include installation of hardware, documentation of networks or other hardware technical specifications, specifications and user help documents for software