Excellent questions dear brother. I will try my best to simply answer them.
I have a question that I am sure you have been asked. Does a person just have to read through the book, or do you require them to come into agreement with everything in the book?
No, but one should agree with the general burden and thrust. Also the statement of faith is important not in every detail of end times events but definitely in the character of God, Christ, Holy Spirit and these things:
http://gospelfellowships.net/pdf/statementoffaith.pdfIs there any centralized authority exercised over any of these remote house churches?
There are no setup list of leaders for the movement. Each fellowship is accountable to the Lord Jesus Christ. And each group has servant leaders as the Lord raises them up. Then as groups connect with each other certain brethren might be looked to in submission to their godliness and walk in the Lord. So in this organic way leadership is recognized not by name on a list on the website. And there is no one leader, certain brethren are simply serving to allow biblical saints to connect with the burden and network.
Are there any other documents that you require these house churches to "opt-in" on or do you just require them to read the book?
Just the principles book and as alluded to above the statement of faith found in the book.
I think it is useful to publish a network of house churches but am concerned about a "mother church", exercising some type of administrative authority over them.
The main reason for not publishing all the house church groups at this point is to prepare for coming persecution. Also to ensure that men do not take charge but the Lord is in charge. So the thinking is opposite in many ways of the way denominations work.
That is why I am asking if there is any more that is required except to tell you, "Yes, we read the book"?
It is not a matter of just reading the book but to share the emphasis and spiritual burdens that we can all agree upon.
Again dear brother, these are 100% great questions and we are very happy to try and answer them as best as we can. Other brothers might also help from a different persecutive to articulate these things. At this point is has been agreed by many of the brothers involved this is a good way to go forward, some things could change but never towards a denominational control.