Ing to Boundy (2012), typically, a written contract will include: Date of agreement. Names of parties to the agreement. Preliminary clauses. Defined terms. Main contract clauses. Schedules/appendices and signature provisions (para. 5).
Writing your own contracts is perfectly possible, and legal. But it's also an incredibly bad idea. There's two reasons for this: Property law is complicated. Because it's such a fundamental part of legislation, it's often lots and lots of different laws layered on top of each other.
If the buyer is not working with a real estate agent and does not have representation, the offer would come directly from the buyer. Represented buyers can also write their own offer letter and have their agent submit it for them.