Every party wall matter is different, each having their own particular nuances. So it would be impossible to list all of the frequently asked questions relevant to your matter. Also, information can be out of date due to developments in the courts, and for this reason we recommend you look at the Faculty of Party Wall Surveyors website rather than rely on posts in Google. The faculty are an important organisation promoting the highest standards of professional practice, and providing education and regulation.
From the FAQs page on the faculty website, I shall draw you attention to the following questions and answers:
"Under normal circumstances the building owner would pay the fees, (known as costs) as he is the one undertaking the works, usually for his benefit. However, the surveyors will make the final determination".
It is worth speaking with your neighbours before any notice is served, and you may be able to reach an agreement that also satisfies their needs and future benefit.
"You are unable to rescind his appointment but you can approach the third surveyor to resolve the matter for you. However, if you have chosen to have just the one surveyor called the 'agreed surveyor', then there is no third surveyor to call upon".
So, there is a financial benefit to appointing an agreed party wall surveyor that acts for both the building owner and neighbour. But, there is no third party wall surveyor to mediate between party wall surveyors! So choose your party wall surveyor(s) carefully.
You have 14 days to lodge an appeal in the County Court. But first enquire with your party wall surveyor or call the faculty for free advice.