I used the 1mm per cubic centimeter as an example the actual expantion is much smaller though im not sure of the exact values.

But the answer is you, your house, the planet are all expanding. As far as I am aware gravity and the strong nuclear force holds us together against that force. Though some hypothosize that eventually the expantion rate will be great enough to tear atoms apart, its called the big rip. Edit: spelling.

Relative distance does change, but the galaxies aren't being pushed apart, rather more space is appearing between them, like a balloon being inflated, if you put 2 dots on the balloon then blow it up the dots don't move, rather the space between them grows, so they aren't moving faster than the speed of light, it is only faster when observed relative to an observer with enough distance.

When it comes to distances far enough out that they are receding away from an observer faster than light can travel the information from them is lost to the observer, without FTL travel the observer could never reach those locations so no information is traveling faster than the speed of light.

No, any local area of the universe isnt expanding faster than the speed of light, rather the collective growth of the entire universe results in the areas further away from you expanding more.

Thing of it as each cubic centimeter of the universe growing by a millimeter per second. The further out you go the more milimeters per second are added but each local area only grows by 1.