Who is responsible for getting approval of cabin layout?
I can answer for the FAA as that is the jurisdiction I am in and familiar with. The FAA (and I assume the other similar organizations) have a variety of guide lines for airplane interiors and its generally on the owner/operator to get them certified. However manufacturers may elect to get an interior configuration certified so that they can sell complete aircraft. As for regulations there are plenty of them, you may want to check this out as well as this and also this. The FAA generally looks at evactuation times (how long it takes every one to get out of the plane in the event of a crash) as well as certain aspects of the seats and restraints. Generally speaking they also look at the materials for their flamability. 

One of the biggest interior policies of recent years was the move to "16G Seats" over the older seats. However as long as the seat is an approved 16G seat it can be used.  

This is a nice summary of some of the research the FAA has done on cabin safety and its components.

As far as I know the FAA will let you submit just about any layout as long as it passes their flame, evac, and safety regulations. With the popularization of large private planes interior options are pretty much limitless. 

On larger planes there are some things that may be fixed like the bathroom and galley since that requires plumbing and electric to be run but its more than likely they can be moved if requested.

There have even been talks of standing room only sections of airplanes but the regulators put a hard no to that as of now.