All offices will accept a walk in application for an extension. Depending on which office you use you may find making an appointment saves you hours in a queue.
Can’t understand where the application is asking for a proof of relationship. If you’re opting for the retirement (over 50) option then there is no need for any proof of a relationship.
If you chose the “marriage” option then it won’t work unless you are physically married. Proof of talking every day would be irrelevant.
You may have read different things Asa retirement extension is 2 months prior but a guardian extension (bar the first one) is 3 months. Both are obtain off the initial Non O visa so could be confusing.