Christmas pics (indoors)

Hello all,

1) Taking pics with my K5 IIs and yes, there are active grandchildren running around. I was thinking that using the Tv or TAv mode with a setting of 500 and letting the camera choose the rest. But the manual says " 1/180 sec. or slower (not faster). Lens is f2.8.
Opinions?

2) Seems the flash does change its output for distance of the subject and I am over exposing. Is there a setting I am missing or do I not understand how to use the flash on this camera?
I would be happy for any help.

-Richard

Pentax K-5 IIs, Sigma 17-50, LX3, Pentax MX w/40-80 & 80-200 lenses, Lightroom 4.1, CS5