Different things are meant by distance,
http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD
and universe,
http://en.wikipedia.org/wiki/Observable_universe#Size_of_the_observable_universe
A center isn't an event, but yes things are moving faster than light relative to other things (namely, us). In special relativity no two things have a relative speed greater than c, but in the more general, general relativity, they can exceed a relative velocity of c.
yes
yes
The radius of the visible universe is less than 13.7 billion lightyears measured in light travel time.