Picky, picky...
Actually, I think Masons have long tried to claim connections with the Templars, so some of these family connections may actually be initially indirect - that is from a Templar uncle or some other relative - but then have been subsumed into the family mythology, particularly if the family was Masonic.
BTW, before offending any Masons on this board, let me note that Masons in Europe are entirely different from what we think of as Masons here. There, Masonry is a very political, anti-religious movement that has frequently allied itself with left-wing intellectual movements to attack the Catholic Church in particular and Christianity in general.
I think so. Several groups could have picked up aspects of Templar existence or claim some spiritual association based on presumed practices.
Most likely the surviving Knights blended in with society and we only see traces of their philosophy today.
I could be wrong :-D
Those are groups not recognized by the United Grand Lodge of England (yes, the initials are UGLE) which traces its history back hundreds of years, and are considered clandestine. Lodges recognized by the UGLE, the origional Masons, are strictly apolitical. Because of the tremendous range of religious and political views of the members of any given lodge, religion and politics are not discussed.