Yesterday 4 hours on train gave me chance to analyse both the slip from the Northern Genealogist, and to complete (in rough form) the transcription of the will (Parts 5&6)
For the tree I get: Generation 1) John Tupholme, William, Jennett(Janet?), Agnes,  Margaret, Gregori, Batte
To deal with the rest of the family, Janet married 

 Stutt, and had 2 daughters Janet and Margaret, Agnes married 

 Coocke, and one daughter Elizabeth, Margaret married 

 Fisher, no children recorded, Grtegori married 

 and had Thomas , Margaret who married 

 Foreman, and Higdon; Batte had no recorded issue.
Now to deal with the main part: Agnes 

 married 1) 

 Fayerfax (fairfax) whose brother was Mayesh; she had George, Humphrey, Thomas and Richard with him, and then after remarriage had William with John Tupholme, William married Frances and their son was Nicholas.So were there 2 Nicholas' i.e. a son and grandson of John, named after Nicholas (1)'s brother? 
Regarding the executors: I suggest Bro.John Bradley (a monk or other cleric) and Thomas Palfreyman, unrelated to the family.
To answer your questions separately: 1) Gregori is the brother of John; 2) Thomas is son of Gregori 3) Geo, Humph, Thos, and Richard Fairfaxare the sons of Agnes with her first husband, and are therefore the half brothers of William Tupholme.4) So far as these documents show Agnes is the only known wife of John. The will shows William Tupholme to be John's brother.
The Boston registers run from  1557 to 1834, so it is well worth searching them for the BMDs of many of these people. I will post the will transcriptions separately.