From the perspective of Gardner Research, all questions are good. We will attempt to collect all of these, categorize them, provide resources for research, and publish results. However, a first step is to look at the long history of work and get the material available in a manner that facilitates further study.
BTW, here is a slogan:
For any domain of study, a closed situation is always suspect.
So, in that spirit, we will organize and foster something related to "all things Gardner." In that context, of course, there will be specific areas of concern, such as Thomas and the mother of his children which is only one of a whole lot of questions to consider.
Now, let's look at the Zouch Phoenix and its passenger list (see image). Son, Thomas, is not mentioned (transcription error?). Joseph was born here. So, who was this Joseph (if the name is correct)?
There are more questions. Later I'm going to put in an image of the birth order by Anderson which agrees with Dr. Frank. That is, Joseph was born after Samuel (Dr. Frank's ancestor).
BTW, NEHGS, your re-configuration to please the mobile crowd made it harder to research from the viewpoint of this old guy (long, long years of collaborative work via the troublesome Internet). It would be nice if these folks would pay attention to the works of human-computer-interface work (did they?).
DAR had the same problem of late. Notice that the TGS site went a little mobile friendly without, I hope, being problematic to those who want to mosey about.
Remarks: Modified: 06/24/2019
03/03/2015 - Perhaps, using an FAQ would be a good start for the most common questions.
03/04/2015 -- Start of a Gardner FAQ as a page.
03/11/2015 -- We will have a larger scope (Gardner Questions) of which the FAQ will be a subset (we envision a large set of essays - included will be links to prior work, of the past century or so). Mentioned above is a collection of topology problems (Pearl, Elliott (2007) Open Problems in Topology II Elsevier) as an example of our usual state of having more questions than answers. This link is to a copy of the Second Edition (1,613 problems). ... The work of one editor but a lot of contributors.
04/07/2015 -- We have more questions than answers (research raises both).
01/18/2019 -- Added to the index at TGSoc.org.
06/24/2019 -- We have started to update the FAQ and will be renovating our sites. With the 400th coming up, plus several years of research accomplished, it is time to pull together a cohesive view some of which will be printed. There is a very long ToDo list that will be published and updated so that others can help us with our tasks. Focus will be on content related to Thomas Gardner, Cape Ann, subsequent events, and much more; plus, we will keep configuration issues in mind which deal with the continual concerns related to technology and information presentation.