You have a few mistakes:

(3) I find the words label and differentiate odd. A symmetry could be broken, either spontaneously e.g. Higgs mechanism, or explicitly.

(4) is a poor definition of a Lie group... as mentioned in the comments, a Lie group is a group that is also a differentiable manifold.

(7) a local symmetry is continuous symmetry for which the continuous parameter that parameterizes the symmetry is a function of space and time. cf. a global symmetry, in which the continuous parameter is constant. For a theory with kinetic terms (e.g. Standard Model), local symmetries are possible only if the local symmetries are gauge symmetries.

(10) As per the comments, the $U(1)$ is an internal symmetry - a particle doesn't move around the $U(1)$ line (parametrized by only one continuous parameter) in the ordinary sense.

Please, somebody feel free to edit this answer to include more corrections or expand mine.

This post imported from StackExchange Physics at 2014-03-07 16:40 (UCT), posted by SE-user innisfree