To answer the first question :
As Raybistre has already pointed out, these are Welsh arms and, in common with Welsh practice, they
do indicate the descent of this Owens family from Hwfa ap Cynddelw, Lord of Lifton, c.1085 to 1169.
When the practice of heraldry was adopted by the Welsh rulers and gentry in the 12th/13th century the bards who maintained the records of the lords' descent "back-dated" the designs to the founder of the line. Thus the various families claiming descent from Hwfa use "his" arms, either on their own (as in this example) or differenced in some way, often by quartering. Another version can be seen in the Arms of the Anglesey County Council which displays the Hwfa arms surrounded by a blue/white border
This unusual, to Anglo-Norman eyes, practice was accepted by the English heraldic authorities and confirmed by the Visitations of the 16th/17th century.
For a more detailed explanation see "
http://www.theheraldrysociety.com/articles/wales/arms_of_the_xv_noble_tribes.htm"
To answer your second set of questions: a Coat of Arms
usually belongs to the senior male line of a family (but there are a few exceptions, as above). In the example you have Owen is the family name , it is not being used as a first name. To take your "John Smith Of Wonderland" : on his death his (eldest) son George inherits the Arms, and so on down the generations as long as there are male heirs. If they were being written up in a compendium they would be described as the arms of "Smith of Wonderland".
As you can see, Heraldry is an interesting and, at times, complicated subject !
Maec