Is this My coat of arms? (Can I legally bear these arms?)
The rules of heraldry vary by country. Under most heraldic authorities, if you can show direct descent to one of the bearers of a coats of arms then you can "inherit" these arms. Take a look at the British heraldic authority web site.
In America there is no legal requirement attached to coats of arms. You may design and display anything you like, including the coat of arms of someone who bore your surname whether you are directly related to him or not. There is an American body that will register coats of arms for Americans, but there is no legality involved here.